To disrespect someone is to act in an insulting way toward them. When you disrespect people, you think very little of them.
Disrespect is all about not showing respect. Actually, it's about showing the opposite of respect, by acting rude, impolite, and offensive. Talking back to your teacher is showing disrespect for her authority. Not giving up your seat to an elderly person is an act of disrespect. So is ignoring the customs and culture in a foreign country. The slang abbreviation dis comes from disrespect and means the same thing.