Indeed. you're taking a low volume signal from the head unit that has minimal distortion and amplifying the crap out of it to get nice clean hi volume sound out of your speakers.

I get that.

I should have been more specific

What is the fascination with amps with the power to cause permanent hearing loss?

If you have to stand outside the vehicle when you crank it, that's just showing off.

Why not just get a really nice lower power amp that doesn't ruin your hearing?

So, in my 05 Ion s2 there's this cable that used to attach to the heatsink of the stock head unit, but my new HU doesn't have an attachment point for this and now I have a slight engine hum when I accelerate and the stereo is playing. I am pretty sure this is caused by this (assuming grounding) cable not being attached anymore, but where do I mount it now?

I would attach it to one of the cover screws on your new head unit.

My main concern about this is my HU is a crappy eBay touch screen I found for like $50 a year or so ago. I'll pull it out and see if this will help, but I didn't want to have to take apart the housing to ensure it doesn't short somehow. You never know what kind of crap they did inside to cut corners and make them so inexpensive ya know? Also I've never installed a HU that has an additional ground like that, I usually install them myself in all my vehicles, so it was odd to come across.

Is it ground?

Check it with a DMM, then move forward.
Most corner cutting mfrs will skimp on the input power filtering (use crappy capacitors), which allows things like this to be present from the start.
On my 97SC2, I periodically have to clean the coil tower post tips where the plug wires attach with high grit sandpaper to remove a thin layer of corrosion that builds w time and causes the hum on AM AND FM.

It is an extra ground to the steel part of the dash structure. I installed a $100 Kenwood in my grandson’s car and had 0 ignition noise.