The first act of a play contains exposition and the inciting incident. In the first half of the first act, the protagonist and other major characters should be introduced.
Obstacles are introduced in the second act; they prevent the protagonist from resolving the dramatic conflict or achieving a dramatic goal. As the play reaches the climax, the protagonist gets farther from the dramatic goal, and the possibility of resolution seems less possible as the action progresses.
The resolution--or fall out from the dramatic climax--occurs in the third act. This may involve a returning to equilibrium in the situation of the play. It may involve a revelation or final plot point.
Arthur Miller's "Death of a Salesman" is a good example of the three-act structure. The play is composed of two acts and a requiem, and it follows the formula of exposition/inciting incident, climax and resolution.
Many modern works of drama are divided into three acts, but they nonetheless retain the dramatic arc of a three act play. A good example is Tennessee Williams' "A Streetcar Named Desire," which was written as eleven scenes, but it contains a distinct inciting incident, climax and resolution.