Homely describes someone who's plain or unattractive, like your homely Aunt Agnes or her squish-faced bulldog.
The adjective homely is a slightly more gentle word than ugly, with a meaning closer to "plain" than "hideous." It's almost always used to describe a less-than-attractive person, and occasionally an animal. If you were British, you'd use homely to mean "cozy and homelike," but in the United States you'd say "homey". Be careful not to confuse homey with homely, or you could accidentally hurt someone's feelings.