What is a heat sink in the annealing process

[Bob Wright]

When someone is using a socket or pipe to hold the brass, they refer to it as if it's a heat sink, this is the part that throws me.

No, the socket isn't in contact with the brass. For anything to act as a heat sink, it needs to be 100% contact with some portion of the item you are heating.
The oldest way of annealing brass was a pan of water leaving the shoulder and neck above the water line would act as a "sink" to stop the heat migration below the water line.
Hope that helps.

 

[243winxb]

A sponge with a hole to hold the case head is my head sink. Wet with water.

 

[Dr. Vette]

I think this is just a "sales pitch". Just MHO

Agreed.