Per Time: "...Today bae is used as a term of endearment, often referring to your boyfriend or girlfriend. Or perhaps a prospect who might one day hold such a lofty position."
The word has been around for years, but was popularized by Pharrell, who released the single "Come Get It Bae" in June:
And now white people are co-opting the word, and frankly, looking kind of stupid.
As for how to use it in conversation, Time recommends:
A good rule of thumb for now at least: if you would use the words boo or babe in some circumstance, you can probably use bae.But if you have to ask, you shouldn't make an attempt. And Michael Che agrees:
This Is What Bae Means, Time
Bae, Urban Dictionary