A typical furnace operates like this:
The thermostat in the living space calls for heat.
The thermocouple sees that the pilot flame is on and allows the gas valve to open. If the thermocouple does not see the pilot (either because there is no pilot or because the thermocouple is defective), the gas valve will not open.
The burners are ignited and a flame is established.
The burner side of the heat exchanger gets hot.
Exhaust gases flow through the furnace flue passages, past the draft hood, through the vent connector, and up through the chimney or vent.
The fan control senses the air getting warmer on the house side of the heat exchanger.
The house-air fan is started when the fan control sensor sees roughly 120F.
The fan pulls 70F air from the return ducts, through the filter and pushes the airpast the heat exchanger.
Warm (140F) air comes out the top of the furnace and is pushed through the supply ducts to the various rooms by the house air fan (Note: blower and fan mean the same thing).
The thermostat is satisfied.
The burner shuts off (but the pilot stays on).
The fan control turns off the house-air fan when the house-air side of the heat exchanger cools to about 90F.
This is a slight simplification and there are some possible variations on this theme. However, this is a common sequence of operation.