From ancient time, men have navigated from what was the only fixed object in the sky, the Polar Star. Holding a piece of wood at arm length was enough to measure the star's elevation over the horizon. Knowing this for a given place, navigators were to follow that elevation until reaching their destination, in an east-west direction. These lines of constant elevation are called parallels, or latitudes.

Sailing in other directions was accomplished by maintaing a constant angle with the star. Later, the compass would help make following these angles much more precise. Lines leading to the Polar Star were called meridians or longitudes. They all converge toward the poles and are therefore great circles that divide the earth into two equal parts.

By convention, a degree of latitude is divided into 60 minutes, or nautical miles. This mile varied widely and the Roman mile was quite inaccurate, leading Columbus to the assumption that Japan was about 4,000 Miles west of the Canary Islands.
In the 15th century, Portuguese navigators, sailing to the Azores and Cape Verde Islands discovered an interesting fact: If you sail say, 100 NM to the north, then the same distance to the east, you will not arrive at the same place as if you had sailed first 100 NM east, then north!
This is because the longitudes are converging at the poles. From this, it became evident that the length of a degree of longitude was equal to the cosine of its latitude. This led to the first trigonometric table, the cosine table that is a necessity for all navigators. It is worth mentioning that, although today's logarithmic tables are used to the base of ten, they were initially computed to the sine value, navigators being the only one who had a practical reason to calculate complex numbers.
While the cosine enables the seafarer to compute his course to destination, it doesn't solve the problem of how to represent graphically the globe on a flat surface that can be used for navigational purposes. Not until Mercator (17th century) came up with the solution of projecting the globe on a cylinder, thus creating the projection that bears his name. Today, all maritime charts are drawn using the Mercator projection. It has advantages but also inconveniences.
The Mercator projection shows true headings. It means that a route can be drawn on a paper chart as a straight line. Indeed, that line will cross all the meridians and parallels at the same angle. A plane, flying such a route of constant angle (also called the rhumb line) - unless on a true east/west heading, will end up in a spiral around one of the poles.

As for distances, the Mercator projection also shows true distances at a small scale. But because it uses a progressive scale, one has to measure distance using the scale (minutes of latitude) at the same average latitude. For longer distances, the Mercator projection may not be what we want, but then: what is a distance? From an aviation point of view, three distances can be considered.

Allow me to work an example: We will be flying from Moscow to New York.

1) The great circle navigation. Imagine that there was a powerful radio station in New York, you can take a bearing on. Because radio waves follow the shortest path, it will lead you to the shortest route. This is the homing quality of radio. This route will take you over Norway and Iceland. Your heading will constantly change, as you cross the meridians at different angles.

2) The route of constant compass bearing. This route is the straight line on the Mercator chart. It will lead you over Belgium and it is longer than the great circle. On the other hand, you may leave your auto-pilot on a constant heading.
3) The route of constant radio bearing. Most of the time, a pilot will fly on a VOR radial. Because these are VHF signals, you will never be able to catch a VOR installed in New York, from Moscow. But for the sake of the argument, let's pretend. If you do fly this way, your route will lead you ... over Spain, thus following an even longer route! This is because you keep a constant bearing to a radio signal that travels along great circles.
From this we can conclude: what is the correct distance measurement on the surface of the globe? The great circle? Yes, because it is the shortest route and the one any navigator would opt for. But unless you home on a radio beacon, the great circle has to be computed for you, either by ... a computer, or with the help of a special gnomonic chart.
Is the X-Plane world really flat? Without opening a can of worms, let me say that, as long as you think of a model in a computer, the world is neither flat nor round, but a succession of bits and bytes! The problem arises when that model has to be translated to a graphic form such as a map, or a 3D rendering of the surrounding.
As you have all experienced, the maps shown in X-Plane have a wedge on the side. This is to account for the narrowing of the meridians toward the poles. X-Plane calculates position as a constant Y-scale (the latitudes) and a varying X-scale (the longitudes). One solution would then be to use the Mercator projection that gives rectangular "tiles" of degrees of latitude and longitude. But it would mean that each latitude must be calculated to its own scale, thus involving another trigonometric calculation. This is possible and it would eliminate the existing error encountered when e.g. trying to align the localiser of an ILS.
One way of calculating this, without putting more load on the processor time, would be to use a look-up table of cosine functions for each degree, then interpolate it in a linear way, in between. Yes, because the "trapezoid" seen in X-Plane maps doesn't have a straight side edge, it is in fact a curve. But if this curve could be seen as a straight line, calculation could be executed so much faster. It would, of course, result in a slight error but not more than a few meters. I think we could live with that, considering that the error would be only absolute, and not relative. If all calculations were done using the same model, ILS, runways, VOR, etc would align perfectly.
However, there is still something that a Mercator projection cannot do for us, namely, polar navigation! Because of its parallel meridians, the Mercator projection meets a limit at the poles. If we want to fly over the poles, we need another system, which is the model that takes the centre of the earth as an origin. This is commonly called the "round earth model" and is what is used in some other simulators.
There is two ways of calculating a position and a route in the round world model, the solving of the spherical PZX triangle - familiar to all astro-navigators - and the linear XYZ model. The former is out of question because it requires too much computer processing time. The latter is the one used, hopefully without too much affect on the processing time, and resulting frame-rate. However this doesn't solve all the problems. Routes of different natures still have to be corrected for what they are in the real world.