"To ante up" means to bet money before you start playing.  In essence, I am paying money to play or betting money to show that I am serious.  This term is used almost exclusively with poker. 

The dealer says, "Ante up."  (Let's say the "ante" is $5.00.)

I put $5.00 on the table to show that I am playing.

NOW the dealer gives cards to all the players and the game begins.  As the game continues I can discard (reject, replace) cards once.  I will have more than one chance to bet.  If I have the best (winning) hand, then I get all the money on the table:  the money the players anted as well as the money they bet.

Please don't tell my mother I told you about this.  She made me promise never to play cards.