A PIECE OF THE ACTION means that someone wants to be involved in some popular or beneficial social activity.
Due to the team’s success in recent games ticket sales have soared, and it seems everyone wants a piece of the action. – (Meaning lots of people want to see the team.)
Studying online is more convenient and often more interesting, so it’s not surprising that the number of students who want a piece of the action is growing rapidly. – (Meaning more and more students want to study online.)