The rump is cut from the end of the backbone. The fillet, also known as tenderloin, is cut from the section of the top part of the cow's back and just in front of the rump - basically between the rump and sirloin, but is also the "back" section of the sirloin. The sirloin is the portion of loin just in front of rump (basically the top mid-section of the cow's back).
All three are considered prime cuts, but the rump is usually less expensive than a fillet or sirloin and is not as tender. The rump is often considered to have better flavour than the sirloin or fillet and can be cooked quickly (frying, stir-fry, barbecuing, grilling, etc.).
Sirloin can be roasted, and is often sold rolled and boned. Sirloin steak comes from the same section as sirloin, but is cut into steaks (T-bone, Entrecote, Porterhouse). Sirloin steak can be grilled, stir-fried, fried, or barbecued.
The fillet is often found in Beef Wellington. It is very tender with little fat, and is used for the cuts referred to as Chateaubriand and Tournedos.