Provided you stay at the monasteries, or you are just passing by at the right time, you will eat meals and dinners with the monks in the monastery's refectory trapeza. The food is normally extremely good, usually vegetarian but with cheese and bread. Mostly you will be looking at bread, olives and vegetables, although occasionally fish or cheese may be served.
For drink, on fasting days Mondays, Wednesdays and Fridays only water will be served. On non-fasting days Greek wine and/or Greek retsina will be available. If you happen to be on the monastery's saint feast day, a piece of sweet cake will surely be available as a dessert.
In order to eat at the monasteries, you must be attentive to eating schedules. These normally take place after their services, that is, after Vespers in the afternoon at around 6 PM or after Divine Liturgy in the morning at around 7 AM. Still, these times are not exact, so you should ask at each monastery for the timetable, and if you arrive after eating times, you may ask the archontaris guestmaster for food.
It is a good idea to take additional supplies with you. They can be bought at Dafni or Karyes, but do not rely on having great variety available. No meat is allowed on Mount Athos as the monks don't eat meat. As a visitor, you will be expected to respect this and not bring any meat products to the peninsula.
You will surely enjoy the food because the monks here are trained specialists at cooking, and the food is all freshly grown and healthy. Furthermore, eating takes place with a monk reading aloud lives of the saints or extracts from the Bible, so even if you don't understand the language, it will be an enjoyable experience.