Eric gave a good a concise description. I'll add that the LEDs you see include both actual sampling rates (44.1 and 48k samples/sec) but also a multiple (176k) Multiples are for when the source (CD player, streamer, really fast typer) "up-samples" the music. This does not increase information, but rather is a trick to move noise out of band and make it easier to design linear, good sounding filters. You may hear of 2x, 4x, 8x oversampling. That's what gets you from 44.1 to 176.4.
I'll weigh in on "44/16 is really very good" though. The problem is often the recording engineer, mastering process etc. I can make a strong case for 24/192 in a studio - it allows for slop in level setting, and for losses while digitally mastering, yet still retains full fidelity. In the home playback equipment it is far less clear.
Typically more up/oversampling is better, but only integer multiples.
I'd spend more time on a good low-noise, low jitter USB/network feed than on bit depth games.
As Eric the pool guy says, digital music is basically a bar chart where the bars are the samples and the smoothed line connecting them is the music. With enough samples its really good!
Njoy