Microsoft DirectX End-User Redistributable or API is a set of application program interfaces for handling tasks related to multimedia applications, especially those planning to play the video on the Microsoft platform. In principle, the names of all the "relational applications" are all began with Direct, such as Direct3D, DirectDraw, DirectMusic, DirectPlay, and DirectSound.

The general term for all the interfaces DirectX application was Direct. After the introduction of the Xbox, Microsoft's relational database application designed for multiple games such as XInput for Mac Mel or replace individual components are designed DirectX published.
Explanations about the different versions of the DirectX:
Microsoft DirectX is more than 10 years and is regularly updated to Mac new resources added to it.
Prior to version 10. The program, DirectX versions were published separately and to download the Microsoft decided it would but then, new versions of the program with Windows new and to a newer version of the Windows programs are new and are not presented separately for download.

Do not install this package on Windows Vista and newer is required? 
As mentioned, Windows Vista and later versions of DirectX and were provided with separate windows for download were not there, but the problem was that the next version will support 10: 9 and earlier versions of Windows had been stopped and later, of 9 and older versions did not support or often result when the game requires DirectX version 9 or older, in its implementation was difficult because it was not the version installed on the system. 
That's why Microsoft has released version 9.0c and previous versions of the program that includes all the updates and install it there, you can run any program that requires DirectX. 
But the point is that if you have a DirectX 9 game or program does not need a reason not to install this package, especially because the new Windows versions support the new Windows 7 and 8.1 as well, and now the game or most applications with DirectX 10 and 11, and 9 version is almost obsolete. 
But if you are dealing with old apps and games or DirectX you want to archive is complete and you have no problem to run games and applications, Mytvanydayn package on Windows Vista, 7, 8 and 8.1 installed. 

Note that this package is included only if it is an older version 9 to version 10 or newer game or application you need to be will make your Windows With this package installed not solve your problem update is ever the version of this 10. After the program has been given by Microsoft to download separately.