A Fragment is a candidate to become a pixel in the framebuffer. For every fragment, OpenGL applies a series of tests in order to eliminate the fragment early to avoid updating the framebuffer.
Most of these tests can be toggled through GL.Enable/Disable, the pages below cover this in more detail. However the most in-depth description of the functionality can only be found in the official OpenGL specification.
The tests are executed from top to bottom, if a fragment did not pass an early test, later tests are ignored. I.e. If the fragment does not pass the Scissor Test, there would be no point in determining whether Depth Test passes or not.