API is Application Programming Interface. In it's generic sense it means that it is a specification for writing code to use some software package that you want to use. In other words, anything that you need to do to write code that uses some particuar software package. It might define certain variables or data structures that have to be set up, it defines all of the methods required to initialize and then actually use the functionality within that package.
There are many differenct APIs because there are many many different software packages/facilities out there to be used.
SCJP - 86% - June 11, 2009