Sure you wear ripped jeans to school every day, but you don't wear them to your grandmother's house out of deference to her. When you show deference to someone, you make a gesture of respect.
The noun deference goes with the verb defer, which means "to yield to someone's opinions or wishes out of respect for that person." If you and your dad disagree about the best route to the grocery store, you might defer to him, and take his route. You're taking his route out of deference to his opinion and greater experience.