What a person ate in medieval times depended on his social standing and on how wealthy he was. Medieval peasants had a very simple diet, and wealthier people had a more varied choice of food.
Depending on what was available to them, people in medieval times might have eaten foods such as eggs, porridge, cheese and whatever vegetables they were able to farm for themselves. They might occasionally have caught or purchased some sort of large game animal, but they were more likely to have access to smaller animals like chickens, rabbits, goats, sheep and perhaps a cow that wasn't being used for milk or work. Wealthier people had access to deer, elk and other large game animals they could hunt or have hunted for them.