Most of the resorts offer numerous dining and bar/pub options, although be prepared to put your hands in your wallet, especially as the operators try to make their money over the (very) short ski season to keep them going through the summer. A lot of the food can be quite unhealthy (chips, pizza, nachos etc), however you will probably find you burn it off with all of the skiing or snowboarding.
Most of the resorts have their own supermarkets, so if you are on a budget, it might be cheaper to buy food and make your own sandwiches to take with you, although again, expect food prices to be high and limited.
If you are interested in a higher standard of food, then most of the resorts have some excellent gourmet dining options, although make sure you book well in advance, as most restaurants tend to be very busy during the ski season.