It's called an enswell but is sometimes referred to as an end-swell, eye iron, endswell, stop-swell or no-swell.
One of the most important tools in boxing, an enswell is a small, cold piece of metal that's applied to an injury to reduce swelling.
It may be kept cool within icewater, or be constructed with a chamber to hold ice cold water. In the latter scenario, the enswell would have to be pre-frozen prior to the bout. However, since ice absorbs less heat than metal at the same temperature, keeping a non-chambered enswell inside an ice-bucket is the preferred method.
How is an enswell used?
A cormer-man or cut-man will apply the enswell using light pressure over swollen or bruised tissue.
The ice cold chill generated by the metal constricts the capillaries to decrease blood flow which, in turn, reduces or minimizes swelling.
Don't use the enswell like a clothes iron.
Excessive pressure, or attempts to "iron out" a bruise, will only damage tissue further and exacerbate the bruise or contusion.
What if unprepared corner-men forget to pack an enswell?
If the enswell isn't packed or and/or the ice bucket its to be stored in is missing, just hope your fighter's face doesn't start swelling during the course of the bout.
The best and perhaps most notorious example of missing enswell occurred in Tyson vs Douglas (1990).
After only five rounds, Mike Tyson's eye began to badly swell and his vision was obviously becoming impaired. But his corner-men, perhaps thinking Tyson wouldn't need an enswell because he was such a heavy favorite over Buster Douglas, didn't pack it.
As a result of Team Tyson's overconfidence, or perhaps incompetence, their fighter suffered a grave disservice.
Woefully ill-prepared, Tyson's corner-men used what appeared to be a balloon filled with water in place of the real thing. And unfortunately for them and their fighter, their efforts were to no avail as Mike's swelling continued.
Tyson would be soundly beaten-up before getting knocked out in Round 10.