Every fundamental and composite particle made up only of fundamental particles has a characteristic mean lifetime. The mean lifetime is a function of a particle's half-life. Both of these measurements of the average lifetime of a particle are a function of what physicists call the "total width" of a particle, which is something that can be measured at a particle accelerator like the Large Hadron Collider, and it has electron volt units, just like fundamental particle masses.
The top quark has a width of 1.5 GeV, and the Z boson has a width of 2.5 GeV. The Standard Model predicts a Higgs boson width of about 4 MeV, which is very narrow. Large widths imply short lifetimes, narrow widths imply comparatively long lifetimes.
The LHC is incapable of directly measuring a particle width this tiny, but it can put an upper bound on it with existing data of about 100 MeV to 180 MeV, that will improve a bit with more data, but will never be all that tight a boundary because the LHC simply isn't a precise enough tool to directly measure a width that tiny, although indirect model dependent estimates suggest that the reality is closer to +/- 14% of the expected value (i.e. a boundary under 7 MeV).
While this isn't a particularly precise measure of the fit of the experimentally measured Higgs boson to the Standard Model expectation, every limitation on the maximum degree to which the experimentally measured particle could differ from the Standard Model expectation limits the parameter space of beyond the Standard Model theories. If your theory predicts that the Higgs boson has a mass of under 125 GeV or over 127 GeV, or has a width of more than 180 MeV, it is ruled out by experiment, even if it matches other experimental data to date. Also, if you theory predicts that a Higgs boson can have a width of less than 180 MeV only if some other parameter X is less than a certain value, this can bound the parameter space of your model.
While the fit of the Higgs boson width experimentally measured to the Standard Model expectation isn't very tight, the fact that this width is so small to start with means that this boundary does have some discriminatory effect, particularly taken together with the whole of the other experimental data we have on the Higgs boson already.