Paul__B:
I think they just put them there to make it look pretty.
Probably.
I use them as jumping points for wires that go outside the board (power wires, jumpers to other boards, etc...) You can solder quite thick wire to them - much thicker than will fit in one of the holes.
You can bridge pads together by putting a wire on the gap between two pads and soldering across it. This makes "power rails" from your incoming power wires.
Paul__B:
Generally, these were for edge connectors,
I think the ones on those boards are a bit too short for edge connectors, especially after you solder a wire to them.
They could be used in a test jig with pogo pins....but It seems unlikely that you'd be producing enough of anything on those boards to require a test jig.