Definition: The set $\{x\in {\mathbb{R}}^{n}|Ax=0\}$ is the null set of A.

Proposition: If p is a vector such that Ap=b, then $\{x\in {\mathbb{R}}^{n}|Ax=b\}$ = $\{y+p|y\in NS(A)\}$

I am just so perplexed by the sudden introduction of notations and all of the null set.

Can someone please explain this in simple terms and explain what the notations are?