A complaint is an objection to something that is unfair, unacceptable, or otherwise not up to normal standards. If your neighbors have a complaint about noise, they want you to be more quiet.
A complaint is voiced objection to something, like a complaint about cold or disgusting-tasting food in a restaurant. Complaint is also a legal term — the plaintiff's reasons for bringing a civil action. Medically speaking, a complaint is a disorder or disease that is hard to cure completely. Loud cries of pain, anger, or sadness can also be called complaints.