APIs

Application Programming Interface. It is a library of specialized functions and datatypes that you can use to write programs.

Do you have a specific question?

An API is the interface for a library -- the types, functions, and data that the library provides. Sometimes people might also use "API" to mean the library itself.

Adding to what has been said, common APIs include -
Direct3D - a graphics API
OpenAL - a sound API

But anything can be an API... If you wrote a collection of useful functions, you could give it to people to use, and call it an API.

The main reason people call them APIs and not just "code libraries" is because usually you only have access to an 'interface' to use the code.

E.g. Direct X gives you the header files, and libraries/DLLs that you can link to (and example source code), but they dont actually give you the source code that was used to make Direct X. This means you can use their headers/libs to call their functions, but you cant edit their code. Hence its an interface that an application programmer can use.

A better way to think what APIs are, they actually serve as an abstraction layer for something more complex. For example, OpenGL is a general purpose (and standardised) library that allows you to utilise graphics hardware without being concerned about the low-level technical details of each graphics hardware.

Alright! Thanks!