With just a diode, you can run it for a little while to see if it fails. Normally if a diode is gunna fail because of a defect, it'll fail early on. Otherwise it'll live out a good 5,000+hour life if driven correctly. You can try running it a bit to make sure it isn't going to die as soon as you ship it out to a customer.
I think the term applies more to DPSS though, where you have crystals to worry about. If you get a freshly made DPSS laser and test it out, let it run for a few hours, and test it again it may have changed significantly. Run it for a while and make sure it doesn't change, and you'll have a good idea of what your stable output is.
Some places don't bother and end up shipping out units that test well when they first arrive, but drop significantly after you use it for a few hours. Burn-in tests help reduce the chance of that (although for some reason I just got back a 30mW 473nm laser I had burned in quite well to find it outputting <1.5mW... oh well