Vertex Colors
Appearance
Vertex colors are, just as the name implies, colors stored on the vertices of a mesh.
Note
They can be edited in blender via the vertex paint mode.
Albedo modulation
The most common use case of vertex colors is to apply them to a materials albedo color and transparency via multiplication

Masking and blending
The second most common use case for vertex colors is to mask or blend multiple layers of textures:

Other
There are also many other applications for vertex colors, but how and which channel gets used depends entirely on each shader.