In the conversation between Rev. Parris and Abigail in Act 1, we learn several things about both characters. Abigail is an orphan and is Rev. Parris' niece. He took her in after her parents' deaths, and helped her to get a job as a domestic (housekeeper) in the Proctor household. She was subsequently fired and has not found another job in the seven months since she left that house. This is disturbing to Rev. Parris, both because it makes Abigail his responsibility (which he does not feel he can afford) and because her dismissal gives rise to gossip. Parris is concerned with his image in the town of Salem, and cannot have Abigail's "soiled" reputation making an impact on him. Add to this the discovery of the girls dancing in the woods, and Parris has no choice but to press Abigail for the truth he wants to hear.
It is after Parris goes downstairs to lead his congregation in prayer that we learn more about the circumstances surrounding Abigail's dismissal. Parris is not off-base when he inquires about the state of Abigail's name in the village.