No maps of the earth are truly perfect representations; all maps have some distortion. The reason for this, is because they are attempting to represent a 3D object (an ellipsoid: the Earth) in two dimensions (a plane: the map itself).
A projection is a representation of the entire, or parts of a surface of a 3D sphere (or more precisely, an ellipsoid) on a 2D plane (or other types of geometry).
Every map has some sort of projection—it is an inherent attribute of maps. Imagine unpeeling an orange and then flattening the peel out. Some kind of distortion will occur, and if you try to fully fit the peel into a square or rectangle (like a flat, two-dimensional map), you'd have a very hard time.
To get the peel to fit perfectly onto a flat square or rectangle, you can try to stretch out certain parts of the peel or cut some pieces of the peel off and rearrange them. The same sort of idea applies while trying to create a map.
There are literally an...