What are pixel shaders?
In their barest essence, pixel (or fragment) shaders are small programmes that take an input image and change the colour value for each pixel. As the code for the pixel shader is a function specified for 1 output pixel (the kernel function), it can only change the current output pixel and does not know anything about the size of the image. These days, pixel shaders and indispensable in video games as they are used to add lighting effects such as Phong shading and normal/bump mapping, or displacement techniques such as parallax mapping. In the context of video games, pixel shaders usually run on the GPU as supported by DirectX and OpenGL.
