like stocks (grips) and recoil, its an individual opinion
A good trigger matters a HELL of a lot, to me.
To me, a "good" trigger is one that doesn't make you pull the gun off target to get it to fire. It can be heavy or light, smooth or gritty, stagey or mushy, but if you can shoot it well, AND IT IS REPEATABLE, then its a good trigger.
That being said, smooth and light (within limits) seems to work better for most people, once they have developed basic skills.
Leave rifle triggers out of the discussion (we're in the handgun forum), and besides, other than generalities, rifle triggers are too different.
Note that the majority of the discussion so far has been about selfdefense/carry class guns, (natural given the dominance of this class of handguns) but there are other kinds of handguns as well. In my personal collection defense/carry/duty class guns (by today's standards) make up only around a quarter of my handguns.
.22 sport pistols, T/C single shots, single action revolvers and magnums make up the bulk of my handguns, and a good trigger pull on them is a necessity to get the most out of them. The rare ones that don't come with a fair to good trigger pull, get one, either from me, or from a professional.
If your handgunning needs are COM at belly to belly range, even a poor trigger will serve well enough. But if you are going to be shooting at greater range than that, (no matter what the target) you need to be able to hit, and a good trigger aids that immensely. A poor trigger (especially one that is not repeatable) actually works against you as the range gets longer.
A good shot can shoot a pistol with poor sights and a good trigger better than one with great sights and a poor trigger, for everything other than face to face combat at speed. And maybe even then!
One of the worst guns I have shot lately was a compact .45 GLock. While the feel of the trigger didn't really give me trouble, nor the reset needed, it was the fact that the gun fired at a different place in the pull, each time, apparently at random. Not repeatable. Pull, bang. Pull, pull, pull, bang. Pull, pull, bang. pull, pull, pull, pull, pull, bang. Pull bang. etc.
That gun went back to the dealer and went away. One can learn to deal with nearly anything, if it is consistant. That one, wasn't. And to me, that the deal breaker, consistancy.
I've got a Ruger Blackhawk .45 Colt (7.5") with a sweet 12oz trigger. Been shooting it nearly 30 years, and can ring the rifle gong at 200yds offhand, regularly. On an auto, that light a trigger would be radically unsafe. I can shoot a 12lb DA pull reasonably well, but its not my favorite. Got some DA autos that have nearly 3/8" or more take up, to a nice 4-5lb pull. Shoot them fairly well also. Each class of gun gets its best from a slightly different "good" trigger.
But what makes a good trigger to you is not known to me.