A shader is a computer program that usually runs on a GPU and is used to do shading, texturing, special effects or post-processing. Shader nodes specifically refer to the nodes used to create shaders for Cycles, but this tag can be used for other shaders as well.
Shaders are most commonly used to produce lighting and shadow in 3D rendering. There are shaders everywhere in blender, e.g. for drawing the 3D view, rendering, etc.