For drawing attention to your posts in the sidebar. It uses a colorful way of presenting posts (what we call quilts) as sidebar elements.
A fair question. The Mini Quilt isn't going to cure cancer or make you rich. But, because it's a visually interesting way for you to showcase your latest works, or a set chosen at random, it could make your blog readers more aware of other things you've published that may interest them, and thus make your blog a bit "stickier"
They're derived from the time of year. Deep winter days are solidly blue, spring is the green time of year, and fall is orangish tones. (These are Northern Hemisphere seasons if you were wondering.) Essentially, every single day of the year has a subtly different color, almost imperceptibly subtle. But if, like most blogger, your publishing is spaced by a week or more and erratic, you'll see very interesting colors side-by-side. (For more on this, I'd encourage you check out my blog, which has a number of posts relating to this algorithm I created.)
A Mini Bar is essentially the same as a Mini Quilt--a visually interesting way to link to your recent (or random) content in your sidebar--but it's stylistically the easiest was to show post titles (to non-hover-aware users and browsers). You can build one with an instance of the Mini Quilt plugin in (the directions are right in the widget control box) or you can use the standalone plugin.