ATM (Automated Teller Machine) is a computer. It has a small display and something similar to a keyboard (even if it doesn't look like one). It runs a program that is usually written by the bank. The program could do anything but banks usually follow a pattern.
Most banks start by asking for the language. They then ask you to insert your card.
This card has a magnetic strip on the back that it reads information about your bank account (sort of like a diskette on a PC). It uses this information to look up your information and decide what to do next. Usually this is to have you enter your password. After that, it's up to the program to decide what to do next.
As for the equipment, banks usually buy the ATM as a single piece but it is actually made up of components. There are several different computer types but let's discuss this as if it were a PC. There would be several PCI slots. Each PCI slot would have a specialized card to support the equipment. One slot would be used for the modem (or network card) so it can be managed from the main office and can obtain information it needs from the central computer where most information is kept. Another slot would be for the card reader where you stick the ATM card in. The money dispenser would be another. I suspect that the deposit slot is part of the money dispenser. The display and keypad probably use the keyboard and display connectors.