Literally, API means "Application Programming Interface." Not too descriptive by any stretch. The Windows API is actually a collection of pre-existing functions inherent in windows that you can call upon to do jobs for you within the windows environment. These functions are stored within the multitude of DLL's that come with our most beloved operating system.
To access these exotic functions, we first have to declare them in our code. The syntax, however, looks a little ugly. Here's an example:
Declare Function sndPlaySound Lib "winmm.dll" Alias "sndPlaySoundA" (ByVal lpszSoundName As String, ByVal uFlags As Long) As Long
The word "Lib" indicates that "a DLL or code resource contains the procedure being declared" and the word "Alias" indicates that "the procedure being called has another name in the DLL." The rest of the declare statement is simply the arguments passed to the procedure.
NOTE: If you intend to declare an API call from within an object (such as a form) you must include the prefix "Private" before the statement.
Ok, so now we have the function declared, and we're ready to use it in code. We now treat it the same as we would any procedure we created ourselves. For a specific example on how to use an API call from within code, see the tutorial on Playing Wave Files.
Where did this magic little piece of code come from? It can be found within the "Winapi" directory of your VB root. Within the "Win32api.txt" file you'll see an incomprehensible list of procedures and constants that make up the API. If you already know what you're looking for, then this file may be useful to you, but generally it's best to read a book about the API or look at web sites in order to find the useful portions.
API calls handling things such as wave output, bitmap display, timing loops and more are explained in the other tutorials available here.