What is this part called for the head lights?

Question

The thing that turns on the head lights

Answer 1

a switch.

Answer 2

Headlight / running light switch - on the turn signal stalk... also the high/low beam switch (headlight dip) that's part of the same assembly.

Or do you mean the headlight relay, which is under the hood?

Answer 3

If it's located seperately on the dash it is simply called a headlamp switch. If it is included on the turn signal stalk it is called a multi-function switch.