Usually it's "give it up for...." followed by the name of the person. It means to applaud (clap your hands for) that person. Why not say 'give' rather than 'give up'? We add prepositions to make things more informal and change the meaning. To 'meet' might sound a bit formal or a bit unclear what kind of meeting it was. However, to 'meet up' with someone sound more lively and it's clear that you're casually meeting friends.

give it up to = give the lead over to someone else