The test points are used by a "bed-of-nails" in-circuit automated test equipment to check that the PCB is assembled correctly.
Typically each surface mount node has a test point/pad associated with it, that is placed on the back of the PCB so that they can be probed with spring loaded test pins. The thru-hole pins can be probed directly. I use test pads that are 0.040" square copper and relieved of soldermask and placed no closer than 0.075" pad center to pad center and preferably on a regular grid and somewhat evenly distributed. At 6 oz of pressure per pin, the forces can add up, and a clamp with a lever is required to hold the PCB to the test fixture. A PCB design I did last week, had 525 test pads and required almost 200 lbs of force to hold it down onto the test pins. I've found it easier to design in the test pads just like any other component but located on the back of the PCB. The test pads can be a real pain to design in after the design is complete. I once worked until 1 in the morning squeezing in 700 test pads after the design was "complete" in order get manufacturing files out the next morning. If the design is very dense, the test pads can be on both sides of the PCB, but this requires a more expensive "clam-shell" test fixture. The reference designators do not need to be visable as the test pad, node and coordinate information is extracted from the ASCII CAD files. The use of test pads is part of "Design for Testability" or DFT.