DTMF is the global standard for audible tones that represent the digits on a phone keypad.
With touch-tone land-line phones, pressing a key on the dialpad generates the corresponding DTMF tone for that key. The land-line phone system can then "listen" and decode that tone to determine which key was pressed, enabling dialing.
Mobile phone networks use digital signals instead of DTMF for direct dialing, but DTMF is still used over mobile phones to navigate automated systems such as phone menus, and for secondary dialing, such as using a calling card.
Each DTMF "tone" is actually two tones - a low-frequency tone and a high-frequency tone - combined. (Hence the name "dual tone multi-frequency".) Looking at the standard phone keypad as a grid, the low tone corresponds to the row, while the high tone corresponds to the column.