"What's ___ story?" is a way to ask for more information about someone who you don't know. It's like saying "Tell me more about that person"
What's that guy's story?
You use this phrase when someone seems interesting, mysterious, strange, or annoying.
You can also ask someone "What's your story?". This is a way to get them to introduce themselves:
A: So, what's your story?
B: I'm a friend of DeAngelo's.