What is the C thermostat connection on Carrier Furnaces
It is one of the 24V wires from your transformer in the furnace. This wire is used to provide constant 24VAC to the thermostat so batteries are not required.
On the list of connections you listed it is Com 24. To connect it you will need to connect one of the wires from the thermostat wire bundle to the Com 24 terminal and the other end of that wire to the "C" terminal on the thermostat. Before doing this turn off power to the furnace so you don't blow the 3A or 5A fuse on the low voltage control side. The common color used on a lot of systems is blue. But it can be any of the wires you have in the thermostat wiring bundle that is not used. If you have no extra wires then you will need to run a new one from the furnace to the thermostat.