Many games of the last 7 or 8 years supported Direct X 9, 10, and sometimes 11. This was due to the heavy influence of Consoles that had 'older' gpu technology. With the introduction of the Xbox One and PS4 and Direct X 11 being the lowest common denominator you will start to see developers dropping support for DX 9 and 10. You will not be able to run games that require DX11 or higher, and as someone else mentioned many game engines rely on a certain level of Pixel Shader, if you don't meet that you will not be able to run the program. (Though you have 4.0)
From a performance aspect you will be fine as long as you feel that games are playable. You can always keep reducing settings.
Games that are coming out right now for the PC probably won't work.
Direct X = Direct3D (They can change the name all they want, but it will always be Direct X to me)
Direct3D 10.0
Shader Model 4.0
(GTS250, GTX 260-295)
Direct3D 10.1
Shader Model 4.1
(210/G210, GT 220, GT 240)
OpenCL OpenCL 1.1
OpenGL OpenGL 3.3