The depth it is referring to is the depth value of a pixel, often (though not always) on a scale of 0 - 1 (relative, although usually nonlinearly, to the near plane and far planes).
This value is used for something called depth testing, or z-testing. Depth testing is an optimization that prevents pixels from being written to the buffer if they would be occluded by something that is closer to the near plane. This also makes ordering of opaque objects less important, and enables many post processing effects that are dependent on depth. This link provides additional information.
Depth testing is an optional step in the rendering pipeline that can be enabled or disabled at will. You will also frequently hear about the depth stencil buffer, which is a single buffer, that combines both depth and stencil testing values into separate channels as an optimization.