In European languages there's a phrase you can say when you or a waiter serves food. For example,
- bon appetit (French/English)
- buen provecho (Spanish)
Does Chinese have a similar phrase?
Yup.
The typical phrase spoken when serving food is qǐng màn yòng
(請慢用). It lliterally means "please eat slowly", but is better translated as "enjoy your meal", and serves the same function as the French bon appétit.
Like Semaphore said 请慢用 is good for very formal circumstances.
In less formal circumstances you can say something like 慢慢吃 - which basically has the same meaning. This can also be used among family and friends.