For simple understanding, it's often helpful to think of electricity flowing through a wire as analogous to water flowing through a pipe. Voltage is like pressure and amperage is like flow. To accommodate more flow, you need a larger pipe but both a narrow pipe and a wide pipe can have the same pressure.
Regardless of whether you have a 14-gauge wire or a 12, the pressure (voltage) is the same. The difference is the amount of flow (amperage) it can handle. This is where the analogy breaks down a bit: when you don't have a big enough wire to handle the flow (amperage), it gets hot, possibly really hot.
To prevent this from happening, we have circuit breakers. They are designed to kill the power almost instantly in the event the flow exceeds the breaker rating. A 14-gauge wire (in typical circumstances) can handle up to 15 amps so if there are any 14-gauge wires connected to a circuit, you need a 15A breaker (or amller). For a 20A circuit, you need all 12-gauge wires (or bigger.)
You are completely fine to connect this to your 20A circuit just don't add any wires to the circuit that are smaller than 12-gauge. That is, don't connect any 14-gauge wires to the circuit.