Hello, AD, this link may be helpful. In that link is also a link to a bit about the 8 precepts that many lay Buddhists observe on Uposatha days, as opposed to the first five precepts that are observed every day.
Uposatha Observance Days:http://www.accesstoinsight.org/ptf/dham ... satha.html
(You asked if the purpose of that precept is about humbling oneself, I think that may be part of it, but if you look at precepts 6, 7, and 8 -- they're all things that we can get "attached to", things that comfort us or entertain us or somehow make us "feel good", which might distract us from the task at hand, our practice, if we overindulge them. These things are prohibited for monks at all times, whereas we laymen are allowed to eat when we want, enjoy entertainment, and sleep in luxurious comfort, but on Uposatha days we choose to step it up a notch and refrain from those things just as the monks in the Sangha do. That's just my take though.)