Players might be more familiar with it's evolved form, Whimsicott, specifically the Prankster Whimsicotts people ran back in the Omega Ruby, Alpha Sapphire meta to set up Tailwinds. Cottonee's inclusion makes sense given the presence of it's version locked counterpart Petilil.
Pokemon GO Cottonee: How to Catch
During the Unova week event Cottonee will have increased spawns and will be hatching from seven kilometer eggs. Eggs currently take half as much distance to hatch so grinding out eggs might be a good use of your time. Aside from that, to catch Cottonee it's really just up to how lucky you get with RNG. You can always try putting up a lure or some incense to boost your chances.
Alongside Cottonee, Sewaddle, Emolga and Bouffalant were added during Unova Week.