Meat is a food staple, alongside plants. Although the status screen lists all edible animal-derived products as meat, the game discriminates them into two categories: true "meat", which is muscle stripped from the creature when it is butchered, and prepared organs, which are just that, prepared organs. The amount of meat that will be produced from butchering a creature depends both on the absolute (how big it is overall) and relative (how big it is relative to the average for its species) size.
Having meat to eat is not compulsory, but important because dwarves like variety, and munching on the same gruel all day will cause negative thoughts. The business side of meat production is handled by the meat industry.