Abandoning a Neopet basically means to disown it and it is permanent so think about it carefully before you decide to abandon your pet. Do note that you can only pound a pet once per day.
People have done so for financial gain, and as stated in the Adoption article, have been frozen. It's strongly discouraged that you create a Neopet, as you may then see another in the pound that you prefer and want to abandon your pet.
Abandoned pets may be readopted by other users. If the pet has a nice name, or has a good colour/species or has high stats then it will likely be adopted rather quickly.