With regards to (digital) audio, high resolution typically means sampling rates / bit depths exceeding 48 kHz / 16 bits (compare to CD's 44100/16). 48k/16 is the least sampling rate and bit depth possible in DVDs that choose PCM for audio, and was at some time even more common than 44.1k/16 in computer soundcards (cf. Intel's AC'97 standard). Given that this format is widely accepted as sufficient as an end-user format, given the limitations of human hearing, the absence of a universally agreed-upon definition of “high resolution” audio need not be of much practical concern, and possibly the least resolution accepted in any widepsread definition is 48 kHz / 20 bits adopted for marketing purposes by the RIAA.
There are "fake" high resolution claims made for marketing purposes, and also algorithms that manipulate the audio to that end - notably has the lossy MQA format been exposed of adding noise to CDDA format files and falsely presenting the doctored file as an "authentic" high-resolution master - but arguably, this constitutes only a next step over lossy files decoded and sold as lossless, or fake SPARS codes indicating that a CD was digitally sourced.