There is no more precise way of knowing your position on the surface of the planet than with a knowledge of your latitude and longitude. Although we talk about degrees, we can divide a degree into sixty parts, which we call minutes. We can also divide a minute into another sixty parts, which we call seconds. So there is no limit to the degree of accuracy that we can use to define out position on the planet.
Determination of latitude is easy because it depends on the position of the sun and the time of day in the place you happen to be. However, the determination of longitude is much harder because longitude is defined relative to the position of Greenwich and can only be found out by knowledge of the exact time at Greenwich. Sailors often had to use what they called Dead Reckoning, a method by which they used knowledge (often guesses) of wind and currents to calculate their speed. Then, with knowledge of time travelled in a given direction, they could estimate their position. However, mistakes were very common and some terrible shipwrecks have occurred, with great loss of life, because navigators thought they were in one place and they were actually somewhere else!
It is too difficult to have a full description of all these ideas here, but suffice to say, that determination of longitude was extremely difficult until accurate clocks were invented. These clocks (called chronometers) were carried in ships and never changed: they always showed the time at Greenwich. From this it was possible to use knowledge of latitude and other measurements to calculate longitude. Today, of course, satellite technology enables this to be done instantly and with amazing accuracy.