The relationship between John and Abigail is a bit complex. It's made clear to readers that John had an affair with Abigail months before the play begins.
I know how you clutched my back behind your house and sweated like a stallion whenever I come near! Or did I dream that? It’s she put me out, you cannot pretend it were you. I saw your face when she put me out, and you loved me then and you do now!
We are never told who initiated the relationship, but that doesn't change the fact that it was completely inappropriate from multiple angles. The Proctor family was Abigail's employer at the time. John is also a married man with kids. He should absolutely know that having sex with a teenager is inappropriate. Elizabeth Proctor discovered the infidelity and had Abigail dismissed. John has worked very hard to secure Elizabeth's forgiveness, and he makes it a point that he will never reach for Abigail again.
Abby, I may think of you softly from time to time. But I will cut off my hand before I’ll ever reach for you again. Wipe it out of mind. We never touched, Abby.
John is adamant that he will remain faithful—however, Abigail isn't willing to accept John's attempt to distance himself from her. She wants John back in her life, and she believes that John secretly wants her too.
John - I am waitin’ for you every night.
. . .
Abigail: I have a sense for heat, John, and yours has drawn me to my window, and I have seen you looking up, burning in your loneliness. Do you tell me you’ve never looked up at my window?
Proctor: I may have looked up.
This exchange does seem to indicate that John may still have emotional or lustful feelings for Abigail; however, he is making a mental decision about what to do. He may feel like acting one way, but he knows what the right thing to do is. It's unfortunate that John had to hurt his marriage so much in order to learn this kind of self-control, but John's mental strength in doing what is right ultimately comes through when he publicly admits to the affair with Abigail.
When Abigail and John Proctor speak privately in Act One, she makes it pretty clear that they did have, at least, a physical relationship when she worked for him and his wife. She reminds him of how he "clutched [her] back behind [his] house and sweated like a stallion whenever [she] came near." In other words, they had a sexual affair.
However, her words also let us know that this affair has been over for some time. Abigail insists that she's been "waitin' for [him] every night," and he promises that "[he'll] not be comin' for [her] more." We learned earlier from Reverend Parris, her uncle, that the Proctors dismissed her seven months ago. More interestingly, though, is that Proctor seems to still have feelings for Abigail. She claims that he loved her when Elizabeth dismissed her from their employ, and that "[he] do[es] now." He admits that "[he] may think of [her] softly from time to time" and that he "may have looked up" at her window once or twice. This makes it seem as though it was not just a sexual relationship that they had but an emotionally intimate one as well.