For me it's means something better than the norm, or at least "better" than what I or other people would consider the norm, but not something exactly necessary per se, that 'little extra cherry on top', if you will. Both flying economy and first class gets you and your worldly crap from airport A to airport B, but first class has better ...everything. So ergo flying in first class is luxury. For example, no would die from sleeping in plain cotton sheets, but compared to that luxury would be sleeping in mercerised high tread count Egyptian cotton sheets, if we are talking about people who usually tend sleep in beds, not some extreme 3rd world examples.
Helps if the stuff in question is limited edition, high quality, exclusive, expensive, hand-crafted by artisans in soft candle light and so on.
Sometimes I find some of the stuff sold as luxury silly. Like platinum beer bottle openers. Sure, it's crazy expensive, hopefully well-made, perhaps designed by some Scandinavian art guru and only 12 pieces were ever made before the designer ate both his hands. I would not automatically call that luxury item. More like pretentious. For me, it would jump straight into luxury category if that platinum beer bottle opener would turn the act of popping off the lid into something very easy, with very little effort, with perfect "hand feeling", compared to normal or other crazy expensive beer bottle openers.
Since it's a fashion forum, luxury clothing is a category on it's own, at least for me. To me, a sweater would be luxury sweater if it was the most gorgeous thing I've ever laid my eyes upon, with it's exclusive pedigree, quality marterial, perfect fit, maybe a known name on the label etc. But just because some sweater costs $1300 and is only available upon inquiry in select Hermes boutiques does not make automatically make it luxury item. That $1300 highly exclusive sweater could just as well happen to be the fugliest piece of pure acrylic that even a color blind brain dead goat wouldn't wear. For me it's just a overpriced piece of trash then. Or different sweater, super gorgeous knit, awesome quality, 100% hand knitted and ever organic. But makes me look like Peruvian tourist guide. No chance I'd consider that a luxury sweater under those circumstances. So it has to be a full set of the above listed qualities to make a luxury sweater. Yes, it's a head thing.
Weirdly enough, old and established names are more likely to be considered luxury stuff by me. If there were two sweaters pretty much identical in every aspect, one made by Marc Jacobs, the other by Lanvin... I would be more likely to rate Lanvin's higher.
I think it even makes some sense.