That is the question, what banged and why did it bang. There's some quantum theories that elude to a possible source of the big bang, but nothing widely accepted. As to why, that's an even tougher question.

The term singularity as applied in cosmology comes from the mathematical definition where one variable approaches infinity as another goes to zero. This is bad in math since it means an equation is not defined across all values. This is what happens mathematically as you get closer to time zero for the big bang. Same with the gravity of a black hole as you move toward the center. In that sense the size of the big bang at time zero would be zero, but the math breaks down so it's not actually defined. Physicists generally believe that's not the case due to the quantum nature of the universe, but we don't have the math to explore it.