An act structure is when a game is divided into distinct acts, parts, chapters, episodes or otherwise called parts with a designated start and stop. In some games the whole game is one act, thus making it a one act structure. Other games have more acts, that are defined by a start and an end, with an act brake between the acts. Usually the drama of a game is focused on different themes in different acts, or just an accelerating drama with a climax and a resolution in the last act following a classic formula dramatic arc. The act brakes may or may not include a time jump.
The act structure of a game is either visible and utilized as a technique in conjunction with the players or it is a technique used by the organizers to decide when organizer controlled events are supposed to happen.
In a visible act structure organizers can focus on different themes or have different rules to create a dramatic shift in the game between acts. For instance, you can have a rule about conflict resolution that varies over time:
Act one, everyone backs down, no weapons are to be fired.
Act two, conflict might be resolved in that someone gets hurt.
Act three, conflict might get resolved by people dying.
The themes of a game can progress in a similar fashion. An example is from Just a Little Lovin':
Act one, Desire.
Act two, Fear of death.
Act three, Friendship.