DirectX is graphics Application programming interface, games, GUI Components, Shaders, VFX are made with it, by programming in it's API
U don't need to pay for it, unless u r a developer & making something commercial with it, U can download the DirectX API & SDK for free from Microsoft, it is the foundation of GUI in the upcoming Windows Vista, even in Windows XP, the GUI is GDI+ based on DirectX 7
for games, directX provides tools & API, much like cement for making a house, u can make graphics with it, game engines which are just rendering engines, anything, any kind of material etc which depends on the shader.
All the games require this common runtime, which can be downloaded for free, even from Non microsoft sources, like download.com or Digit CD/DVD