Abigail starts her web of lies in a desperate attempt to not be held accountable for her nefarious deeds in the forest the night before the play opens. She had been out in the woods dancing (forbidden in Puritan communities), AND casting a "charm to kill Goody Proctor." She drank chicken blood and cast a charm hoping to dispatch of her mortal enemy, Elizabeth Proctor, all in the hopes of securing her current love, John, for her own. So, when Parris and others find out about the dancing, and about the spell-casting, Abigail is afraid that she is going to be in deep trouble. As Mary Warren states fearfully, "Witchery's a hangin' error," and if Abby is charged with witchcraft (which would have been the most accurate charge of all of them, interestingly enough), she will be hanged. She doesn't want this. She has threatened her girlfriends to stay quiet in the hopes of avoiding this.
As Abby is mulling her possible demise at the end of the noose, Tituba is being coerced into confessing to witchcraft herself. But then an interesting thing happens. As soon as Tituba confesses, she isn't whipped, hanged, or even chastised. She is blessed and praised. And as soon as Tituba starts naming OTHER people as witches, it takes all of the focus off of her, and she is praised as in instrument in god's hands come to save them all. Hmmmm, Abby thinks--I can confess to witchcraft, accuse OTHER people of being witches that made me do it instead, and I not only won't get in trouble for what I did, but I will also be praised and adored? I think I'll give it a go! So that is the original reason that she starts accusing others.
She continues in order to keep her posse of girls in line with fear--with each accusation, the town loves her and believes her more, granting her more and more power. The girls know, as Mary Warren states at the end of act two, that if they try to back out, Abby will "turn on" them and accuse them of being a witch. Keeping power and control keeps Abby safe. Then, you can't deny that Abby seems to be a bit of a drama queen who loves attention. Abby also holds great bitterness against many of the townsfolk for being such goody-goodies, so that plays a factor too. She also has to build up her accusing reputation, if you will, so that when she finally gets around to accusing Elizabeth it will be believable. If she only accuses Elizabeth, that would be too suspicious, but if Elizabeth is just one of many evil witches in town, no one will really notice it as anything different.
All of these factors lead to Abby being a ringleader of one of the most notorious gangs of accusers in American history. I hope that those thoughts helped a bit; good luck!