These system listen for the same messages that tell the system what number your are dialing and need to be connected to in the first place.

Originally in the day of rotary phones that was pulse dialing but that has long since been replaced by something called DTMF or touch tone.

This system came along with keypads replacing dials. It sends out a combination of two tones for every button you press.

For example all the buttons in the uppermost row of the telephone will produce a 697 Hz tone while all buttons in the leftmost column will produce a 1209 Hz tone.

So pressing one will result in a tone that is a combination of 697 Hz and 1209 Hz. Something like pressing the 5th F and the 6th D Key on a piano at the same time.

The device on the other end can listen to these tones and recognize them.

In the old days these tones were simply send across in the same channel as the normal sounds you make when talking into a receiver.

Modern systems with VoIP can send these signals along as data in a separate channel.

When the system was new people could actually imitate those tones and confuse the automatic switches that listend for them by whistling into a receiver.

That was useful as there were additional tones that for example told the switchboard that somebody had paid money in a pay-phone.

If you knew how to whistle a 2600 hz tone at an AT&T switchboard from one of their payphones you could make phone calls for free.

This was called phreaking.

The buttons work by sending out two tones, the combination is unique for each key. The equipment on the other end interprets the tone.

You can see the tone and how they are used at https://en.wikipedia.org/wiki/Dual-tone_multi-frequency_signaling#Keypad

[removed]

Each one makes a slightly different sounding bleep or bloop, and the computer recognizes the tone.

What you are calling is a computer or what they call Interactive Voice Response (IVR) listening. Each key pressed has its own assigned tone. The computer matches the tone with the number pressed. The computer then routes that customer support call to a human that is pre-assigned to that number that has the skills to answer the questions of the number chosen by you. The technical term is called Dual-Tone Multi-Frequency signaling (or DTMF). In customer support centers humans are assigned to those (queues) numbers based off of skills sets that have knowledge in different areas of the business.