It was somewhere outside Barstow when igor
wrote:

When a company says that its clamp can extert X amount of force, what does
that mean?

Average hand force to twist the handle generates that much linear
force.

This is generally a combination of the helix angle on the screw
thread, moderated by the bendiness of the frame.

It says that the clamp "Exerts up to 250 lbs of clamping pressure".

Well they're lying.

And they're Irwin, so don't buy it anyway.

I've used this clamp and tightened it as best I could by hand, squeezing the
trigger. Assuming I have a "normal" strength grip, would that mean that at
that point the clamp is exerting 250 pounds?

No, see my previous point about "lying".

These aren't usually bad clamps for lighter gluing, and you don't need
250lbs to clamp a glueup anyway, or else you get squeezeout. But
leave it a few months until the pawl wears and you're lucky to get a
few lbs out of this type of clamp. The best ones I've found are by
Wolf (turquoise and black) and even those don't last very long.