Sticker packs contain party stickers which are used to level up parties. You can win them from various sources such as the spin, bonus rewards from other features and parties themselves!
There are 2 types of sticker packs; green and purple ones. The green packs are normal ones which provide random stickers. Please note that duplicates might come out of this pack but you earn some rewards if it's a duplicate sticker; so there's no losing! The purple packs can be bought with cash on the party popup and they provide you with unique stickers. So, you will 100% get a new one that you don't already have.
As you collect stickers, you'll see that they go to your parties on the popup, so you can level up parties with them. When you have all four parts of the same color for a party, you'll level it up!