DirectX is basically used for graphics effects (it's also used for audio) and in general it enhances how the graphics looks. However DirectX 11 (DX11) depends on a few things:
1. You need Windows Vista, Win 7, or Win 8. Win XP only supports up to DirectX9.
2. You need a DirectX 11 compatible graphics card. The Radeon started to support it with the HD 5000 series in 2009. GeForce started to support it with the GT/GTX 400 series in 2010.
3. The game itself must be designed to make use of DX11. If you play a game that only supports DX9 (like Fallout 3), then you will not see difference.