Various issues. One is the volume in general, the other is the volume at different frequencies, a third is being able to clearly hear people against a lot of background noise..
A cheap hearing aid will just increase the overall volume in a crude way.
However, most people like me who have worked with rock drills and fire-arms don't lost their hearing evenly, but lose all the high-frequency (high-pitched) sounds more than the low frequency (deep, base) sounds. So more expensive hearing aids increase the high-pitched sound more than the low-pitched sounds so as to compensate for this.
Also, most older people have increasing trouble hearing one person speak against a background of other noise (eg lots of people speaking as at a party or in a shopping centre). Expensive aids detect the individual voice(s) and amplify it (or supress the background sounds). A proper audiologist will actually tune your new hearing aid to fit your individual hearing. I found that what had previously been a general background noise in a shopping mall previously, became individual voices (I could suddenly identify which person each voice was coming from, it was no longer a single blurred sound - I could hear what individuals were each saying across the width of a shopping mall.).
Yes, hearing aids are expensive. But cheaper hearing aids will not be nearly as effective - buying a cheap one over the counter will probably be rather disappointing compared to the possible improvement you could achieve. But of course you may have no way of knowing that.