There are rumors that Elizabeth Proctor does not like Abigail Williams because of the fact that Elizabeth dismissed Abigail from her family's service seven months prior to the start of the play, and the fact that no one else has inquired about hiring Abigail since then makes it seem as though Abigail did something wrong. Reverend Parris himself has heard that Abigail's presence in church is the reason that Elizabeth no longer comes to services.
In Act Two, however, Mr. Hale asks John Proctor, Elizabeth's husband, to account for the fact that they have only been to church some twenty six times in seventeen months, and John tells him that his wife was sick this past winter, and that this kept them away.
Early in the play, in the first scene of Act I in fact, a rumor is discussed regarding Elizabeth Proctor's reasons for staying away from church.
Parris is speaking with Abigail about Abigail's troubled reputation in Salem. She has been fired from the Proctor house, raising questions about her character, and soon afterwards Elizabeth Proctor stops coming to church - the purported reason being that she cannot be so close to Abigail as to share the same church building with her.
When Parris questions Abigail’s character, he mentions that she was dismissed as the Proctor’s house servant. Rumor has obviously circulated in Salem that she was dismissed for unseemly behavior and that Elizabeth will not come to church and sit near “something soiled.” (eNotes)
We discover soon afterwards that Elizabeth is upset with Abigail because of the affair Abigail was having with Elizabeth's husband, John Proctor.
Thus the antagonism between Elizabeth and Abigail is articulated early in the play. This interpersonal history is important in that it demonstrates that many of the accusations of witchcraft that are eventually made (like the one Abigail makes against Elizabeth) are based on personal grudges and not actual fears of witchcraft.