A Spanish speaker asked me for the English translation of "Buen provecho." I laughed, and when I asked some friends the same question, they laughed, too. The reason is that the obvious translation of "Buen provecho" into English is... "Bon appétit!" Like many other words and phrases relating to cuisine, we have borrowed a French expression. There are a few others: saying goodbye to someone leaving on a trip, we may say "Bon voyage!" or "Au revoir!" And when sending out an invitation to a dinner or other occasion, when we want people to let us know if they are coming so that we will have a "head count" for the number of dinners that will be served, we use the initialism "RSVP," which stands for "répondez s'il vous plaît." It is possible that many English speakers do not even know the French phrase; RSVP has become almost a word in itself, and has even been transformed into a verb: "Please RSVP to Dan at [phone number]."
"Bon appétit" is an invitation to enjoy the meal that has just been served, and as a French expression suggesting haut cuisine, it would be used for a fairly fancy meal.
On further discussion with friends, we decided that there was, however, two possible equivalent phrase. One is simply: "Enjoy!"
And another would be "Don't stand on ceremony! Dig right in!" You would hear this at an informal dinner... a family gathering at Thanksgiving, or an outdoor dinner on a backyard patio. The interesting thing to me is that this is by far the most frequent use of the phrase "Don't stand on ceremony." "Ceremony" here means that it is polite to wait to start eating until everyone has been served and the host and hostess are seated. "Don't stand on ceremony" means "I'm giving you permission not to be polite." "Dig in" is an informal expression meaning "to eat your food," with a slight suggestion that it would be OK to take big bites. "Dig right in" means "go ahead and eat right now."
I'm just a U.S. native speaker, not an expert on regional English, and all such usages are regional so other English speakers may have comments about this.
