Modern latitude and longitude is what allows us to navigate the world's continents and oceans today. How these came to be makes for an interesting story!
I jump between the two terms in this post, which can get confusing. I mixed up the terms a few times myself, but don't worry! I fixed the errors and shared a key below to help:

Graphic by Djexplo, shared via Wikimedia Commons. Licensed Use under Creative Commons CC0
Latitude is "USES LATERAL LINES and is calculated by Altitude."
Its lines on a globe are lateral (horizontal) lines.
Ancient civilizations used the altitude of stars to calculate latitude.
Similar to the word altitude, it tells you how far up or down you are on a globe in terms of North and South.
Longitude is your location as you "WALKING ALONG the Equator."
Longitude tells you where you're at from East to West, such as if you walked along the equator.
Its lines are the vertical bars on a globe.
Ancient civilizations--as early as the Phoenicians in 600 BC--estimated latitude by the stars to sail the seas! The Polynesians, a civilization I wrote about some months ago, did the same thing much later, in 400 AD and beyond.
A variety of instruments were developed over the centuries to accomplish latitude measurements, including the gnomon, Arabian kamal, back-staff and cross-staff, astrolabe, and the quadrant, sextant, and octant. These methods used the relative altitude of stars such as the North Star or the Sun--their height above the horizon--to determine a person's latitude, how far north or south they were. During the day, most of these instruments required a person to look directly at the sun. It was common for sailors throughout history to develop bad eyesight or even blindness because of this!
Longitude proved to be a more difficult problem to solve. Longitude had to be cracked at sea so sailors and explorers could combine latitude and longitude measurements. This way, they could navigate anywhere in the world with confidence as to where they were, even after weeks or months of sailing the open oceans. So in 1714, Great Britain's Parliament offered a grand money prize of 20,000 pounds to the person who could achieve the calculation of longitude at sea within half a degree--in recent U.S. years (calculated around 2017), the prize would be equal to about 3 million dollars.
Let's cover for a minute how longitude works. Longitude measures distance from east to west. There are 360 degrees of longitude that span all the way across Earth (in mathematics, 360 degrees is the angle that spans a circle's entire circumference, or exterior). Longitude divides Earth's circumference.
Mathematically, each degree of longitude is divided into 60 "minutes", and each "minute" is divided into 60 "seconds". These "minutes" and "seconds" are simply terminology for units originating from ancient civilization. When these terms are used for longitude, they are measuring angles in a circle, not time.
To calculate longitude within half a degree would mean to be accurate within 1 section of the Earth out of 720! Now, this may have given miles of opportunity to calculate longitude accurately enough to win the modern equivalent of 3 million dollars. But calculation of longitude required a "reference" point that changed reliably when traveling East and West.
Latitude was much easier to solve, and had been solved thousands of years before, because when traveling North and South, the location of the stars in the sky changed reliably. These provided references that could be used to accurately discern one's northern or southern location. The necessary reference to calculate longitude wasn't solved yet, though there were three known methods at the time that could be used to change that.
Observe the movements of Jupiter's moons while traveling for a period of time.
Observe the movements of Earth's moon while traveling for a period of time.
Find the difference in the local time from other locations' local times (the most convenient comparison was to use local noon, such as 12:00 PM in Eastern vs Central Time).
The first two methods required astronomical tools and calculations that didn't come to exist for another century. Further, because each method relied on time measurements, the contenders needed to have accurate clocks. The problem? There weren't any that worked on the ocean!
The clocks of that day were ticked by swinging pendulums, such as those in grandfather clocks. Longitude had already been solved on land with pendulum clocks back in 1667, but the waves that rocked boats at sea proved to make a pendulum clock very confused. Even Isaac Newton, a world-class physicist long remembered by history, proposed that this limitation in technology couldn't be overcome.
Here entered John Harrison, a clockmaker in Britain who would change exploration--and consequently the world--in all entirety.

A painted portrait of John Harrison by Thomas King in 1767, later engraved by Philippe Joseph Tassaert. Public domain, via Wikimedia Commons.
John Harrison was born in 1693. He grew up fascinated by the clocks of his time. The watches of his day were large, and one could easily see its gears. He grew up observing their internal workings and helping his father, a carpenter, fix the clocks that were occasionally sent in for repair. Eventually in his childhood years, he had learned enough to take apart clocks and put them back together himself. In his adulthood, he became a clockmaker and designed some of the most accurate clocks of the century. One of his professional goals, understandably, was to develop a clock that would work accurately at sea and win the longitude prize.
After five years of toil, his first marine chronometer, the sea clock "H1," was produced around 1735. It received approval by the Royal Society of Britain to be tested on a route to Portugal, Spain in 1736. The tests went well; Harrison's invention accurately predicted longitude on the trip. But Harrison's inventions had to prove their worth on transatlantic routes (routes across the Atlantic)--this first trial wasn't long enough.

Left: H1, the first sea clock and the invention that first glimpsed a chance at obtaining accurate longitude measurements.
Photo by Phantom Photographer and shared via Wikimedia Commons. Licensed use under Creative Commons, CC BY-SA 3.0
To gain opportunities for his inventions to be tested on transatlantic routes, he began improving on the original sea clock's design. He found flaws in his inventions, though, and spent over twenty years developing H2 and H3. They were never fully perfected. Around 1750, Harrison began working on a much smaller and more portable marine chronometer: a sea watch.
On left: H2, photo by Tatters ❀ from Brisbane, Australia and shared via Wikimedia Commons. Licensed Use under Creative Commons CC BY-SA 2.0.
On right: H3, photo by Bin im Garten, shared via Wikimedia Commons. Licensed Use under Creative Commons CC BY-SA 3.0.
H4, Harrison's first sea watch, took six more years to build. But it was given a first trial voyage to Jamaica in 1761. On the voyage, its ability to support accurate, transatlantic longitude measurements was proved--after over a decade of effort, Harrison had won the competition! The British Parliament, however, held back the prize money, arguing that Harrison's success might have just been a stroke of luck. Thus, Harrison's inventions had to undergo still more trials.
During this period, Harrison invented H5, an upgraded version of the sea watch that also proved dependable. Again, the British Parliament withheld the full prize. They even changed the Longitude Act so that the full prize would only be awarded once other accurate marine chronometers had been produced, further proving their reliability. Eventually, after petitioning the help of King George III, Harrison was awarded 8,750 pounds--less than half of the full prize--by which time Harrison was 80 years old.
Left: John Harrison's sea watch H4, photo by Phantom Photographer and shared via Wikimedia Commons. Licensed Use under Creative Commons CC BY-SA 3.0.
Right: John Harrison's sea watch H5, photo by Racklever at English Wikipedia and shared via Wikimedia Commons. Licensed Use under Creative Commons CC BY 2.5.
Harrison died three years later. And as for the full prize? It was never given to anyone.
Harrison's life work was invaluable to the maritime world, and his marine chronometers were soon widely used. Captain James Cook used H4 on his second and third voyages; he is especially known historically for mapping the Hawaiian Islands and certain regions of Australia (including the Great Barrier Reef), America, New Zealand, and other islands throughout the Pacific. Later, the inventor John Arnold improved upon Harrison's marine chronometers, making their production cheaper and ensuring their widespread use in shipping. Other inventors continued to produce newer, cheaper, and more reliable marine chronometers over the following century.
Today, navigation via latitude and longitude is simple. Satellites are the new "reference" for their calculation, while computer programs do the calculations for us. As a result, any individual in the world can view their exact location merely by the push of a button. But our world would not have been explored, mapped, colonized, and transformed into what we see today without the contributions of a single clockmaker nearly 300 years before our time--a man by the name of John Harrison.
Sources:
On latitude tools:
Gnomon
Kamal
Back-staff and Cross-staff
Astrolabe
Quadrant, Sextant, and Octant
Some more details about latitude
Why latitude was much easier to solve than longitude
https://www.sea.museum/2016/06/22/look-to-the-horizon-why-latitude-was-easier-to-find-than-longitude
History of latitude, longitude, and John Harrison
James Cook
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