Vertex Shaders and Fragment Shaders are both feature of 3-D implementation that does not uses fixed-pipeline rendering. In any 3-D rendering vertex shaders are applied before fragment/pixel shaders.
Vertex shader operates on each vertex. If you have a fixed polygon mesh and you want to deform it in a shader, you have to implement it in vertex shader. I.e. any physical change in vertex appearances can be done in vertex shaders.
Fragment shader takes the output from the vertex shader and associates colors, depth value of a pixel, etc. After these operations the fragment is send to Framebuffer for display on the screen.
Some operation, as for example lighting calculation, you can perform in vertex shader as well as fragment shader. But fragment shader provides better result than the vertex shader.
