It was a standard and certification introduced by Japan Electronics and Information Technology Industries Association (JEITA) in 2014. Specifics can be found here:
https://www.jas-audio.or.jp/english/hi-res-logo-en
While it's not a bad thing that something is certified, it doesn't necessarily mean much. The reason is that while there is some evidence that people physiologically respond to sound above the range of what they can hear as pure tones (young people typically hear up to 20kHz, and as you age you loose much of the ability to directly hear high tones, for men they start loosing the high frequency perception in their mid-30s, for women it's a little later), it's both tricky to capture high frequency sound (every mic, every mixer, every bit of recording and mastering gear has to be capable of and set up to preserve and pass along those high frequency sounds) and since sounds above 20Khz aren't directly perceived by people, without spectral analysis of the full frequency range who knows what's been captured in a hi-res audio file - maybe it's great, maybe it's got leftover high frequency noise as a side effect of some mastering/mixing mistakes. Things get even more confusing because the music studios have a tendency to remaster recordings when they release them in Hi-Res, so unless you personally take that Hi-Res master and then downsample it yourself to a non-Hi-Res format and then conduct your own double-blind tests on the right playback equipment comparing the various versions, you won't really know if the Hi-Res recording is better because it's captured and reproduced more of the frequency range or if it's better just because it's been remastered. I think the best candidates for recordings that might actually be worthwhile to have in Hi-Res are modern recordings of orchestras made from the beginning with the intention of being a Hi-Res recording, but I haven't done enough comparisons/tests to weigh in on whether I think it's really worth the bother (something I plan to try to do someday).
At the end of the day, it's one of those badges on a product box that can impress a casual consumer, and while in theory if everything you bought was Hi-Res certified you should be able to play back music with frequencies above the directly perceivable range, it would depend a lot on particular recordings whether there's anything of consequence in that expanded range. I wouldn't worry about it too much.