Meat can be found in the icebox in the Mammology Lab. Though you can show it to many of the characters in the museum and get humorous responses, its only actual use in the game is in the same room it's found. You need to use it on the steamer trunk immediately after opening it to avoid being attacked by startled dermestid beetles.
The dermestid beetles will then carry off the meat and occasionally be seen in the Museum Hall (Bottom Floor) or the Sun Altar Room still carrying the meat. Fortunately, one will not have any further need for the meat beyond this point.