(someone) is on a diet

Being "on a diet" means that you're following a strict set of rules about what to eat and not eat. People mostly go on diets to lose weight or to improve their health.

"Going on a diet" is different from "having" a diet. Everyone "has" a diet, which is simply the foods that you usually eat. For example:

I'm the first to admit that I have a pretty unhealthy diet.

This means that the speaker usually eats unhealthy food.

This phrase appears in these lessons: