I'm in calculus right now, and personally, I would not have wanted to skip College Algebra. There's a lot more algebra involved in Calculus than some people realize at first. Things like finding derivatives and limits basically turn into a huge mess of algebra at times, and without a rigorous understanding of the algebra behind it, it can get complicated. Professors will always treat Calculus in different ways, but a solid understanding of trig functions and trig identities is pretty important too. My professor loves trig, and uses a lot of it in his Calculus lectures and exams.
I learned a lot in College Algebra. It tends to be a lot more in depth than previous algebra classes were. You usually get a pretty rigorous treatment of both conic sections and logarithms, do a decent amount of work with sequences/series, cover a lot of concepts like minima/maxima that become crucial in calculus, amongst many other topics.
The modeling part most likely refers to applications of the the topics. Things like using exponential/logarithmic functions in biology for modeling population growth/decline, modeling bacteria reproduction rates...other things like how to use conic sections in their countless applications.