The first meaning of action means raises and bets. Assuming there is a 3rd heart and it hits the board with a lot of action, this could be seen as a player making a flush. The second defines action to mean the opportunity to make an act whereby if there is a player who seems not to know that it's his or her turn, the card dealer may politely tell the player that it is his or her time to act. To make it clearer, the dealer says something like "Sir, it's your time to act."
A table that has lots of action is one that has lots of raises, re-raises and bets which means an action is done when money is placed in the pot. Betting action is essentially part of the term action. Like in many cardrooms where poker is played, you are likely to hear a player say "I raise" which remains binding and calls for an action. On the other hand, to receive action refers to when another person places money in the pot and you expect to win that hand.