The characters begin the play a little tipsy and keep drinking until dawn. Some seem to have real alcohol problems while others drink just to avoid the horrible tensions of the evening. The ever-present theme of alcohol seems to be another example of how people hide from the world. For the characters, being drunk is just another illusion, another way to avoid the uncomfortable truths of their lives.
By forcing Nick to make her drink in Act 3, Martha is expressing power over him.
George continually enables Martha's alcoholism because it gives him power over her.