The Quick Answer
Putting a steak on a black eye does not help the black eye to heal in any way. In fact, it can be dangerous, since the steak is raw and potentially home to hostile bacteria. Putting such a thing onto cracked or open skin can be harmful to your health! Sorry to all those who may have received this "remedy" in the past; the truth is, you healed all on your own (and you wasted a good steak).
But Wait--Steak Worked for Me!
In the old cartoons, steak is slapped onto the face of an injured character to help heal a black eye. The steak always appears fresh and raw. This type of thing would never have really helped one bit. However, some people who swear by steaks fail to realize that what was actually helping the black eye was the cold--so they typically grab a steak out of the freezer, then press it against the eye. In this case, the cold acts to bring the swelling down. The steak itself does nothing, and could even be harmful.
The Real Remedy
When treating a black eye, the most useful remedy is probably to pack ice onto it to bring down the swelling, then take it easy for a while. Taking some mild anti-inflammatory medication might not be a bad idea, either. The wound will heal itself quickly. If you must use a steak, make sure it is frozen (as good as ice) and wrapped in a bag or some other material that can prevent your skin from actually making contact with the meat itself.