Each letter on the keyboard corresponds to a number that has been assigned to it called a scan code. The operating system software maps this scan code to a Unicode, so when a particular scan code is typed, it knows which character to use.
Unicode is just a standard that allows the computer to associate each character with a number that never changes. This number is different from the scan code, and there are enough numbers in Unicode to assign numbers to the characters in many different languages.
The actual display of the character is carried out with a "font." In its simplest terms, a font just tells the computer which pixels to turn on or off for a given character.