Nail stickers mainly function as nail art. You typically buy them in pre-cut sizes that cover your entire nail, or as decals or appliqués that add pattern and design to your existing nail look. One of the great things about nail stickers is that you can achieve intricate and artful details on your nails without paying a nail artist a lot of money to create them. This savings also means that you can afford to change it up more often. Unlike polish strips, some nail stickers have a little dimension to them so the patterns often look like they've been painted on. The decals usually come on clear sheets that let you look at different placements on your nails before peeling them off. The stickers are supposed to be easy to remove, usually just by soaking in warm water and peeling them off -- and the big bonus is they don't damage your nails. They're water resistant and if you use clear polish over them, they'll last a lot longer.
One of the big cons is the sizing and application process. The stickers come in one size fits most and the proportions don't always match up with your nail dimensions, so you may have gaps on the sides. Decals can be tricky to get on just right, especially when working with your non-dominant hand. If you apply stickers near the tips of your nails, they'll chip along with your nail polish, so it's best to keep them on the nail bed. One of the biggest pros is that they're quick and easy, but if you want to add shine that nail polish typically provides, at minimum you'll still have to apply a clear base coat. And while the stickers do come with an adhesive back, it's not meant to be permanent, so if you want them to stay on for a while, you'll also need to add a clear top coat. Neither of these are deal breakers, but they do add a little more time and effort.