Action has two common meanings. In general, it means the amount of money being wagered, as in a heavily bet game having plenty of action. For one player, it can mean their total bets over a session, which is larger than their net loss or win because the same money is bet many times. In US sports betting, a bet that stands and is not cancelled or voided is said to have action.
Example
A player starts with 100 units and bets 10 units on 40 roulette spins. Their action is 400 units, even though they only ever held 100.