An adoptable is a character design created by an artist for the purpose of transferring to other people.
When you buy an adoptable artwork, you get rights (e.g. a license) to use the artwork, which allows them to use the artwork for roleplaying, using as a reference for future artworks, etc. However, the artist may place conditions on the use of the artwork, such as where you can uploaded it, if you are allowed to alter the artwork, and most commonly a requirement for attribution (credit). Adoptable artworks also often have terms regarding gifting and reselling (often that the adoptable cannot be sold for more than the original purchase price, to prevent scalping).
To use an adoptable artwork on Star Army, you will have to comply with the artist's terms.
On Star Army, adoptable artworks should always be credited when used in a page. Links are not required unless specifically required by the artist.
Adoptables can easily be found on DeviantArt under the DeviantArt-related > Devious Fun > Adoptables category. You can also find anthro adoptables on FurAffinity. Adoptables are usually sold for cash (via PayPal) or DeviantArt points (a micro-transaction currency that also is cash-based) at a set price, in an auction, or via accepting offers. There is usually a strict time-frame for sending payment.
Here's some terms you need to know:
Here's an example for crediting, using the art on this page: