Cheese is an item that can be found in the mousetrap in Wolf Heimlich's office. To safely obtain it, one must use an object to trigger the trap from a distance.
It is described as being a wedge of the finest Limburger cheese. "The ultimate in cheesiness." Closer inspection reveals a spot of mold on it. Olympia Myklos also notices the spot of mold when asked about the cheese, and notes that given enough time, it will completely consume the cheese, then die itself of starvation.
Later in the game, Laura Bow and Steve Dorian encounter a group of rats in the Sphinx Tunnel leading from the Furnace Room to the Tyrannosaur Exhibit. Merely tossing the cheese to the rats is not sufficient - the rats will still be present and dangerous, and go after Laura and Steve.
Instead, Laura has to toss the cheese into either the left opening or the right opening at the end of the tunnel. If Laura throws the cheese into the left opening, the rats will follow it, and there will be the smell of something burning, indicating the rats have been burned in the furnace. If Laura tosses the cheese into the right opening, then the rats will follow it onto the floor of the Tyrannosaurus Exhibit room and then scurry off.