Crushed ice is used to cool drinks, and is often applied to injuries where there is swelling, to remove excess heat generated in the tissues.
Heat from the skin goes into the ice, and melts it. As more and more ice turns into water, more heat is used up. Water can store a lot of heat. The water acts as a storage device for the heat energy.
Our question is: 'why does crushed ice cool something faster than large cubes of ice?' Crushed ice in your drink cools it faster than ice cubes, and crushed ice will suck heat out of your swollen leg faster than big blocks of ice. Let's look at the reason why.
There is now three times as much area for the heat energy to enter the ice and start melting. The result is that the small pieces of ice can absorb heat faster. So your drink gets cooled faster, or the heat from your swollen injury gets removed faster.
Exactly the same principle is involved when you break up a substance into tiny pieces in order to make it dissolve faster in a liquid. Find out more about this topic here.
In actual practice with an injury, it's impossible to wrap your swollen leg around all six sides of a big ice cube, so the cube doesn't provide its full surface area for cooling. The smaller pieces, on the other hand, can be molded around your leg, and more of their total surface area can be brought into contact with your skin, allowing them to cool something faster than a big chunk of ice would.