"Getting wrapped up in" something means that you pay a lot of attention to it.
This can be something like an interesting story:
I'm on the third episode of the season. I'm getting really wrapped up in it.
It can also mean becoming involved in something that you don't want to pay attention to:
A: They seem to be having a lot of problems. Do you think we should help them?
B: It's best not to get wrapped up in it.