Some household appliances, such as air conditioners, are controlled by relays, which use small voltage to control large voltage. Is the voltage of the air conditioner high? Why use relays?

Your understanding is somewhat one-sided. Relays control large voltage or current with relatively small voltage (this is a vernacular, not a scientific definition). In air conditioning, this small voltage is output by the computer version, which is generally 12 or 24v direct current (DC). The relay controls the compressor to turn or stop. The working voltage of the compressor is 220V AC, that is to say, the electricity working at different voltage values is mutual. So, you should understand.