'up themselves' or 'full of themselves' are ways of saying 'having an inflated opinion of themselves', 'thinking they are more important or better than they actually are'.

Can you provide the entire sentence? Is 'up' perhaps part of a phrasal verb?

It means to love themselves more than they love others. To have a high opinion of oneself. Literally: 'a persons own penis in their own anus' 'to have sex with oneself' - derogatory, offensive.

It is more polite way to say "up their own arse" which means they think are better than others.