So, the full version of this sentence would be "O kadındır-She is a woman." and the -dır can be dropped while not necessarily effecting the meaning of the sentence. The -dır is most likely included as an alternative translation.
Does adding "dir" to the end of a noun make it a verb meaning "to be a (noun)", or am I missing something?
It's not really adding the "to be" because sentences without -dir will still mean "to be (noun)" It's simply emphasising the statement and/or fact. The -dir doesn't change the meaning of the sentence in itself, so you can omit/include it as you wish. For example;
O çok güzel. (S/he is very beautiful.)
O çok güzeldir. (S/he is very beautiful.)
As a native, I can distinguish that the second sentence is just more "fortified" in what it's trying to say. Does this make sense?
Also, please read about it more here. https://www.duolingo.com/comment/7738500