A good example of a collection of API's is DirectX. You have Direct3D, DirectSound, DirectInput, D3DXSprite, etc... All of which are different application programming interfaces (API's) that make up the DirectX SDK (software developement kit).
The DirectX API's are meant specifically for, well pretty much what their names imply. Direct3D allows a programmer to use a list of predefined functions and classes that are used to draw 3D images to the screen. DirectInput allows the programmer to use functions that check for and handle input from different input devices.
However, as many previous answers stated, C++ is not the only language that can access these API's.
If you were using PHP, you would think of an API as being sort of like a premade file of classes and functions that you include in your PHP scripts to more easily work with other interfaces such as the video or sound card hardware (dumbed down version).
If you know ANYTHING at all about HTML, then you already know that HTML has absolutely nothing to do with programming. All HTML does for PHP is allow the data returned from the server to be interpreted and displayed by the user's web browser (we could get into .hta files, but that's further than I want to take this). HTML is merely the logical form of the visual structure of a webpage and is merely a mark-up language.