The more the excursion, the more the distortion. The better subs will have more control of themselves at the higher excursion. That is, they have a larger linear region. One way of looking at xmax is where the sub goes from linear to non-linear. Also known as where the distortion becomes audible. Hearing this exact point varies from person to person, but there is a generally accepted measurement that extrememly few may be able to detect it below.

IIRC, it's necessary to have 4 times the displacement to create a frequency an octave down. So bass, especially the bottom end, takes a lot of displacement.

There is some more, but I'm not sure if I can explain it without getting technical. If you keep popping specific questions, I may be able to avoid that. I'll explain what I can.