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.