What is a map projection?

Answer 1

It is a projection of a map.

Additionally

A map projection is used to represent all or part of the round Earth onto a flat surface which always creates some form of distortion. Mapmakers and mathematicians have devised countless ways to project the image of the globe onto paper.

Answer 2

A map projection is a method for taking the curved surface of the earth and displaying it on something flat, like a computer screen or a piece of paper. Map makers have devised methods for taking points on the curved surface of the earth and "projecting" them onto a flat surface. These methods enable map makers to control the distortion that results from creating a flat map of the round earth.