I'm trying to understand DFAs is my DFA correct in this question if not why?
This dfa is incorrect. 
To start, a dfa MUST define a transition for every node, including accepting nodes.

Anyhow, the current dfa would have accepted the language L = { w | w is a series of 1's and a single 0 at the end }

To correct this, you need to add another transition from B to A when it recieves 1 and a transition from B to itself when recieving 0. This is required to allow strings with 0 in the middle to also be accepted