How Does Up-Sampling Work?

[hfvienna]

But I am confused as to what and how up-sampling works and how it could even create a better quality analog signal from the original digital signal.

Upsampling of course can't produce a better quality file , because the quality is not getting better if you take everything times 2 or 4 and divide it later again by 2 or 4. But it definitely can help , providing a file with a higher sampling frequency, which leaves more space between the highest parts of the sampled signal and the critical point where - due to the nature of decoding - the limit of usable area ends. So the decoding process can be managed with not so steeply rising filters, which diminishes the phase distortion of the signal. In other words you don't gain quality at producing the higher sampled file but in decoding a file in a softer manner.