'Where am I?' might seem like a simple question. In these days when an increasing number of smartphones have a GPS receiver, all you have to do is press the appropriate button and it tells you exactly where you are. The trouble is this information isn't a lot of use on its own. It gives you a geometric position: using triangulation from a number of satellites, it works out where you are in relation to the centre of the earth. That's better than nothing but, pace Jules Verne, you're not very likely to go anywhere near the centre of the earth, so knowing where you are in relation to it isn't much help. What you really want to know is where you are on the surface of the earth, particularly in relation to all the other places on the surface of the earth: where's this town or that lake? where have I been? where am I going? So what you really need is a map that relates your position to the rest of the earth's surface.
"How far's the nearest pub?" might also seem a simple question. Your GPS device can give you your position. So now all you have to do is find that of the pub, and subtract the two. That gives you a distance in, er, degrees, so you just have to work out your latitude and how many miles or km a degree of longitude corresponds to at that latitude. Even if your GPS device is very clever and able to calculate this for you, that too isn't much practical use, as it's the straight-line distance, and you're unlikely to be able to travel in a straight line to get there. So here too you need a map to work out how to get from where you are to the pub, a map drawn to scale in a meaningful measure of distance, so you can work out how far that is on the route you will be taking.
Drawing a map too might seem like a straightforward task; all you have to do is get GPS coordinates for all places and then draw them in the right place at the appropriate scale, no? Well, no, it's not that simple. For a start, it's impossible to properly represent a curved surface like the earth on a flat map. You have to 'project' the curve onto the plane, which will inevitably introduce distortions. Also, the earth is not a perfect sphere, so a projection that might fit the actual earth's surface in one place won't necessarily fit somewhere else. So, over the years, cartographers have come up with a wide variety of models of the earth, together with a wide variety of projections to try and map their part of the world accurately, or at any rate to keep distortions to a minimum.