when chinese people who practice ancestor worship make a food offering what happens to the food (read detail)?

It depends. If it's for a celebration (ie. New Years Day, Mid Autumn Festival, etc.) then people eat the food after the ancestor worship.

But, if the food is used in a funeral, then the food is thrown out after the worship. Eating food that was used to worship a deceased person at their funeral is a big no-no.

Alot of oriental societies furnish meals to deceased family members. My lifestyle, which isn't chinese language, does this at Christmas, the place if any family contributors member has gave up the ghost that year, a plate is placed on the table for him/her, and meals is placed on it. To me, it merely shows that those genuinely everyone isn't forgotten, and reflects the theory as religious beings now, the transition from this life into yet another life is completely recognized and was hoping for. In community American customs to boot, a plate of meals is presented to God. this is a reminder that he's actual to them and worth of acknowledgment, for in this worldwide, God is seldom recognized in daily life. In Celtic lifestyle, a tumbler of wine or whiskey is poured out onto the floor for an identical motives. there are a number of cultures who "ancestor worship", different than to me, as a sort of cultures, this is greater a comprehend for people who bypass on, and need for an after life. no one truly worships spirits.

some food is eaten as a sign of respect...
some food is just thrown away (animals or beggars may make use of it)...
some food is thrown into the river (and eaten by fish naturally)...

Ok, it depends. Some people just leave the food there(If there is not much and the food is not good). Some people take them home and eat it(if there is a lot and the food is good). I am a Chinese. Believe me.