"Action" as used in gambling typically refers to a bet or wager or just the general act of betting. More specifically, "action" can be used to mean either a live bet/bets or, in poker, a bet along with any calls for that bet.
Action may also refer to the total amount of money wagered by a player in a full gambling session. And in sports betting, a bet may be deemed "action" if it is valid. In baseball, "action" is a special type of bet wherein the bet still counts even if there is a change in starting pitcher, which is accompanied by a change in odds.
"Now, if any of you would like to take a long shot on the dog collar, we'll take that action."