What does the idiom on a mean?

The idiom "on a" isn't a complete idiom. It's likely you're thinking of a different phrase, perhaps one of these:

* "On a roll": This means to be experiencing a period of success or good luck.

* "On a whim": This means to do something suddenly and without planning.

* "On a budget": This means to be careful with spending money.

* "On a mission": This means to be determined to achieve a goal.

Could you please provide more context or the full phrase you're thinking of? That will help me understand which idiom you're referring to.