I'm installing 240 volt in-floor heating mats. The amperage draw is 21 amps. I intended to connect them to a 2-pole, 240 volt, 20 amp breaker. My thought was that you have two legs of 20 amp power (40 amps total). Is this correct of how the 240 volt breakers work?

NO. You do not add up the amperages.

A two-pole 20A breaker is 20A @ 240v, or 4,800 potential watts
A single-pole 20A breaker is 20A @ 120v, or 2,400 potential watts.

Since electric heat has to be figured at 125% you need a two-pole 30A breaker wired with #10cu wire. You only need two hots and a ground. You do not need a neutral for this 240v circuit.
10/2NM cable would be typical.