In the example above, the speaker uses "this" instead of "a". There's a small difference between the two. When you say "this ___" it sounds like you're talking about one specific thing. "A ___" is more general.
You use "this ___" instead of "a" or "the" when you're introducing something specific that you're going to talk about. It's usually used at the beginning of a story or explanation. For example:
Amy and I were sitting there talking and this guy I know walked by.
I've had this song stuck in my head for two days!
Today I was talking with this girl at work who just got back from maternity leave.
In all of these examples, the speaker will continue by telling a story about that topic.
People only use "this ___" in this way in casual spoken English.