Dual-tone multi-frequency or DTMF is the group of special sounds a telephone makes when you push the buttons. Each number button makes a different sound. Telephone company equipment hears each sound and turns it back into a number. When all the numbers in a phone number are pushed the telephone company equipment will make the other person's telephone play a loud sound so they can answer their telephone and talk to you.
Telephones also have a star (*) button and a pound (#) button. These buttons also make different DTMF sounds. These buttons can be used for other things like 'go' or 'do over'. But they are not part of the phone number.
A few telephones have the letter buttons A B C and D. They also make different DTMF sounds.