Why is it called "base" leg?
Traffic pattern (circuit) phases are named so that they do not cause confusion1. I think of it as the leg which is taking me towards my landing/home base. (It is just a memory aid.)

However, the following reason is the best one which I found:


  This leg represents the foundation for the final approach, that is,
  the base from which the final approach is initiated.


Another reason is as follows, although it is similar to a memory aid:


  ... base leg is called “base” because it is really the foundation of
  your landing (the “base” of a house is its foundation – and if it
  isn’t right, the whole house will never be right) – if the base leg
  isn’t right, your whole landing will suffer for it.




1: Although, upwind leg, crosswind leg and downwind leg relates with the wind direction too. But if wind is perpendicular to the runway, downwind leg is not actually downwind, but it is still called the downwind leg.