How does E-Test at a PCB Fab work?

As I understand it, they extract a pad-list and netlist from the gerbers, and then have a machine with robotic arms carrying test-probes (Termed "Flying Probes") to manually ohm-out all the connected nets.

See:
http://en.wikipedia.org/wiki/Flying_probe
http://www.spea.com/ElectronicsIndustryTestAutomation/FlyingProbeTesters/tabid/108/language/en-US/Default.aspx
http://www.youtube.com/user/speamovies (Really cool videos)

Some manufacturers also use a "bed of nails" tester. This measures the resistance / conductance from locations on the PCB board surface to other points on the surface. From the Gerber files they know where there should be conductance and where there should be opens.

E-testing is primarily used to detect bad plated holes, as this is the most common failure as it's more process-sensitive. Bear in mind that a flying-probe e-test rarely checks for shorts as it requires a huge amount more checks (therefore test time) than a continuity test - each node to each other possible node. Probably easier on a bed-of-nails tester which has connectivity to all nodes at the same time. I've certainy had a few supposedly e-tested boards with shorts.