Quick answers:

Quantization is the process of altering sounds to 'snap' the sounds to the designated timing. For example, if you play four quarter notes, and then quantize to the quarter note value, they will be perfectly placed, timing-wise. Without quantization, they would be looser, timing-wise. Some quantization is useful in some situations to clean up messy playing, such as to the nearest 32nd note, but too much makes the music lifeless and sterile - too perfect - unless you're going for that sound, like techno. That's a very quick and dirty explanation.

Mastering is a much more complicated subject. The short answer to your question is, it depends; every song is different. A slightly longer answer is that mastering is a separate process, after the song is done, to alter the sound. One purpose might be to equalize the tone or volume of a song so it fits better with other songs on the same CD. Another (mis)use might be to squash the life out of the song (remove dynamic range, the difference between loud and soft sounds) so it plays as loudly as it can and sounds as loud as other songs on commercial radio.

Hope that helped a little. More specific questions can get more specific answers.

BIAB 2025 Win Audiophile. Software: Studio One 7 Pro, Swam horns, Acoustica-7, Notion 6, Song Master Pro, Win 11 Home. Hardware: Intel i9, 32 Gb; Roland Integra-7, Presonus 192 & Faderport 8, Royer 121, Adam Sub8 & Neumann 120 monitors.