Here is the heat sink from my computer. It's made of aluminium and has a fan on the top. Notice that it is not solid. It is made of thin layers of metal to give it a big surface area. More on that later. Computers have miniature circuits which overheat easily. That can destroy delicate components so they need to lose thermal energy quickly and efficiently.
Notice that under the microprocessor mount there is white paste. This is conducting paste/ It means that the thermal energy from the microprocessor conducts easily into metal. The metal conducts thermal energy because it contains free electrons. These are able to go on ahead to hit other atoms and make them vibrate. Remember that conduction is when one atom hits the next and makes it wobble!
The large surface area is to enable the thermal energy to be passed on to the air by conduction. Then there would naturally be convection in the air. It would become less dense and rise. The fans speeds up this process. It removes the warm air quickly and replaces it with cooler air. If cooler air is touching the hot metal then the conduction process will go more quickly. If the metal and the air became the same temperature then there would be no further net conduction. The fact that the aluminium is silver means that heat radiation is not an important process. In fact, it could cause problems by being absorbed by other parts inside the computer and causing it to overheat.