The phrase is used when someone is not paying for something out of their own money. Usually it would be their employer who would be paying, for example when they were having a business dinner.

It's on expenses = the company will pay, it's free so eat up!

expenses = money the company gives you to buy stuff (usually for the company) In this case, the company paid for the dinner.

Dear Olga; Respects! I am agree with Barbara, for better understanding I tell in another way: For example you and me are in a job travel that all expenses are payed by company. But you dont know. in dinner or ... you declare your worry of expanses. I say : - Don't worry, it's on expenses it means that like last expanses this is by company! Be happy!