I'm not sure what the Collections are either. I imagine it's just like things you gather sort of as an "achievement" type thing.
I got this game a while back when it was free. There's a lot of people that like it and it's got good reviews on the App Store, but I could never get into it.
After games like Pizza Boy and Miss Claire Garden, I guess I expect a little more from my Mario-esque platformers. Maybe it just felt a little too geared towards kids (even if it isn't necessarily easy).