What is a projection?
Globes are the best representation of the earth because all distance, areas, and shapes are proportionally correct. Unfortunately globes of any size are rather inconvenient to tote about and store, and detailed images of even a large country would require globes larger than a room. Using portions of a globe would work but they still don't lie down flat and would be like trying to store large potato chips (potato crisps) of all different sizes in book form.
To deal with this problem ancient peoples created maps. The earliest maps only showed very small portions of the earth and were very serviceable without worrying about spheres and such nonsense — indeed, they were not made as replacements for globes at all. But the Greeks had grander plans and by at latest 600 BC the idea arose of projecting the globe onto a developable surface. This launched cartography, the science of mapmaking. A developable surface is a surface that is capable of being unrolled onto a plane. Without allowing a surface having ripples, creases, or tears (all of which have critical drawbacks), a cylinder; a cone, and a plane (which was 2-dimensional to start with) are the only three objects that can be developed.
These three surfaces give rise to the three natural projection classes that have members — true projections — which can be displayed physically by projecting a light source through a transparent globe onto a developable surface used as a screen. The classes are called cylindrical, conic, and azimuthal (because all azimuths from the center are straight lines and their directions are true).
Within the natural projection classes are many projections that cannot be projected physically, but rather are derived mathematically. They still fit within the three classes because they have similar appearances and obey certain critical mathematical rules. Any representation of the globe or part of the globe on a flat surface, such as a sheet of paper, can be called a projection.
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The equirectangular, or plate carree projection, is the simplest possible geographic projection: the identity function. It is neither equal-area nor conformal, but is sometimes used for raster data.