Catch up is a phrasal verb and so the two words should not be separated in this context.
Therefore, we are not dealing with the word catch as in catch the ball,
but rather catch up as in If you run fast enough, you might catch up to the others.
Here, catch up means to close a gap between yourself and someone who is ahead of you.
When we use it in this sense, we are catching up to the time that has passed; Since last I saw you, many things could have happened to me so my 'life story', in a way, has moved on from what you know. When you meet me and I tell you what has been going on, I catch you up, meaning 'bring you up-to-date'.
The important thing then to realise is that catch and catch up are not the same.