It's a colloquial phrase meaning roughly "to explain to sb" but you are not explaining something they don't understand. You are more explaining to - or perhaps a better word would simply be "telling" - them something that has happened while they have been absent, so that they can "catch up" with the news i.e. become current with the situation.
Can someone catch me up with what you talked about while I was on the phone?
I'm sorry I missed the night out this weekend - you need to catch me up on all the gossip!
It feels like I've been on holiday for a month not a week - catch me up with what's going on with you.
Student or Learner