Or a set of kitchen plugs has gone out because of the GFI hiding behind the heavy hutch in the dining room or nook. The point of this is to see if the device is still sensing properly, so as to do its job of stopping electrocutions.
In this diagram the GFCI to the left is hooked up so as to sense and protect other outlets besides itself. S., and in some respects in Canada, GFCIs have been required since 1973 to protect more and more locations in new homes. This does not mean that each location requiring such protection has to have its own GFCI device.
Normally there is continuity between neutrals and grounds at a receptacle, because both are ultimately attached to the neutral bar at the main panel.
However, if a GFI receptacle has interrupted power to other "normal" receptacles, one result would be that a continuity test between neutral and ground at such a receptacle would show very high resistance (no continuity).
Recent GFCI design requirements seem to be making the test button unnecessary: new GFCIs must fail to deliver power if the GFCI becomes incapable of reacting properly to faults. Of course, they can fail in other ways, as when they WON'T run things. Above all, DON'T THINK THE GFCI IS DEFECTIVE WHEN IT KEEPS TRIPPING or will not let itself be reset.
I have come across only two cases of defective tripping.