For example, you can ignore an unkind comment by not acknowledging it. You can avoid an unkind comment by not talking to the person in the first place. You can ignore an irritating sound by focusing on something else. You can avoid an irritating sound by going someplace else that is quiet.

Avoiding is staying out of someone's way; completely acknowledging their existence but trying to stay away from them, and ignoring means you can be in their presence but pretending they don't exist.