The unit with the dial is called the regulator.

The thermal switch thingie is called a thermocouple.

What typically happens is that spiders cause the pilot tube to restrict the gas output and the flame won't reach the thermocouple. If the thermocouple doesn't sense heat from the pilot light, it shuts off the gas to the pilot light. This is so that you don't blow up your house.

So, you just get in there and remove the pilot light tube and check for spider webs. Clean it out thoroughly, reinstall it, and the flame should reach the thermocouple. After the thermocouple heats up, you can remove your finger from the override button on the regulator, and the pilot light will remain lit.

Then turn the dial on the regulator to "ON" and you'll have heat via the main burners.