Why did mammoths have tusks?

There are a few reasons why dinosaurs have horns.

Defense. They have to be able to defend themselves in case of an attack.

To look fierce and vicious to scare off predators.

To make other dinosaurs be scared to keep them away from themselves.

Helpful tools when roaming or moving something.

There are other things, but those are the things I know.

-----------Edit

Current theories are that dinosaurs used them for aggressive displays to ward off competitors or to attract mates, much as animals with horns do in modern times. This is a convergent evolutionary theory.

However, in days past, it was believed that the horns were probably used for defense or attacking. This is considered highly unlikely because of the lack of serious damage to fossil remains that would be caused by this behavior.