key elements of this play, we don't get to directly observe the action, and we can't see into his mind. All we have to go on is what he says, and what Abigail says, and perhaps the generalatmosphere and general human psychology. Abigail talks about being a "wild thing." Perhaps he was drawn to her wildness. She also accuses his wife of being cold; perhaps John was frustrated in bed. Perhaps it was the boredom of a small community. Perhaps it was the fact that he should have power over her, and there is a long history of men who have power using it for sex. Perhaps it is that she wanted him so badly that he was tempted. 

Elizabeth Procter actually reveals the best information that we get about this question.  John Proctor never explains why he does this other than revealing that he did once lust for Abigail and stating that his wife was sick.  However, in the end of the play – Act 4 – when Elizabeth is asked to get John to confess, she does blame the entire affair on herself.  She says, “It were a cold house I kept.”  Basically, she is telling him that he should not blame himself for what he has done because she was a very cold, unloving person toward her husband; she seems to feel that she drove her husband away from her and toward the only other woman who lived in their home – Abigail.

In the final act, when John and Elizabeth are talking, she alludes to some possible issues that had prompted the affair.  She says, "I have sins of my own to count.  It needs a cold wife to prompt lechery", perhaps referring to the fact that she was a stern, unkind woman, who was not very loving to John.  She admits that "I never knew how I should say my love. It were a cold house I kept."  So, she was not very openly loving, and had a hard time expressing her love for John.  This, in combination with the fact that she had been "a long time sick", might have driven John away from her into Abby's arms.  It doesn't justify the act, but at least gives us a clue as to some of the reasons why it happened.  

We can't leave out the Abby factor though.  If nothing else, this play shows her fierce determination when getting something that she wants.  She wants John so badly for herself that she shoves a needle into her own belly to set Elizabeth up.  Who knows what sort of scheming she did in the actual household when she worked there, in order to tweak situations into her favor.  All in all, the affair was highly unfortunate, and leads to some very disasterous situations.

By this stage in the play John's getting pretty desperate. The way things are going both he and his wife Elizabeth are heading for the gallows. So John somehow has to undermine Abigail's credibility as an accuser. Getting Mary Warren to spill the beans didn't work so he openly admits to having had an affair with Abby.

John's confession is supposed to provide the court with a rationale for Abby's making all these false accusations. She's a scorned woman who wants revenge. In Puritan communities at that time there was a double standard when it came to adultery. Although it takes two to tango, as it were, the woman involved was always blamed for any affair, and would be labelled a "scarlet woman," or a "temptress." John knows this, which is why he reveals the affair.

Unfortunately for John, his gameplay fails miserably. Elizabeth, thinking that she's protecting her husband's reputation, denies that such an affair ever took place. Unwittingly, she's just made John look like a complete liar and fantasist in front of the whole court.

I assume that you are talking about the time that John Proctor admits his affair in public (in Act III) and not whenever he admitted it to his wife (not actually seen in the play).

If that is what you are asking about, he is going to disclose it mainly to get his wife and others out of being accused of being witches.  He wants the court to know why Abigail has been doing the things that she has done.

John's attempt to be honest backfires when his wife does not back him up -- she's trying to save his reputation but ends up hurting him instead.

On one hand, I think Miller might have added this fictional affair because it provides Abigail with a really concrete reason, a very strong motivation, to continue making accusations: she wants to eliminate John Proctor's wife and have him all to herself. Abigail's willingness to accuse innocent people like Elizabeth really characterizes her as incredibly manipulative, conniving, and malicious.

On the other hand, Miller might have added this fictional affair because it problematizes the character of John Proctor. He is not some perfect and guiltless man; he is a sinner, and he feels terrible guilt for his affair with Abigail. John initially thinks of himself as a fraud as a result of his affair with Abigail, and his struggle to regain his self-respect and sense of his own goodness is a major component of the play.  His internal conflict is, in many ways, even more important than the external conflict. It is, in the end, John's personal redemption that matters most to him (and to Elizabeth)—so much so that he is willing to trade his life in order to retain it. Without his and Abigail's prior relationship, John would likely be much less relatable because he would not have such personal struggle. John's weakness humanizes him.