What exactly are adoptables and what all can you use them for? I'm interested if you can set them as your horses image? or is it only an avatar thing?

Depends on the shop, some are for your bio, some are just because, some are sets, avis, horse avis.

An adoptable is a character design someone creates and sells for someone else to use as their own. Where and how you can use the design you purchased depends on the individual seller. Typically they are reference images for making art or stories of the character in the future. Some people may offer them as stable sets or horse avatars. Really, you just need to ask the seller you want to purchase from what guidelines they have for the use of the design.