How many percents of the money wagered on the game a bookmaker pays out to customers. E.g. if the payout rate is 98%, then the bookmaker will keep 2% (margin) for themselves and pay out 98% to customers. Alternatively, they keep $2 out of every $100 wagered and pay back $98 to customers.
The bookmaker's cut of a bet. Margin = 100% - Payout rate.
Vig is another word for margin. So vig-free = margin free. Vig-free odds = the odds when the bookmaker's margin has been removed.