What is cylindrical projection?

Answer 1

It's a geometrical technique for plotting the 3D spherical shape of the Earth onto the 2D, flat, plane surface of the map.

In most forms it imagines the map sheet is rolled into a vertical cylinder of diameter (scaled) = Earth's scaled diameter, so tangential to the globe all the way round the Equator. This means the longitudes will be accurate along the Equator, but the latitudes will be increasingly inaccurate with increasing angle North or South if plotted at equal intervals. Therefore the latitude lines are plotted at increasing spaces N & S, to correct for the error.

Now, a moment's thought will show that if the longitude lines are plotted on a circumferential pitch (linear distance) at the Equator they will be hopelessly out as the plot approaches the poles. So the longitudinal, or Equatorial, axis is plotted in angle increments: still not correct but the better option.

It is something of a fudge but projecting irregular shapes littering the surface of an oblate spheroid onto a rectangular plane can only be an exercise in minimising approximations!