Artist's proofs are simply a more collectible subset of a limited edition. Originally, artists produced their own prints using very primitive printing technology. They handcarved an image into a plate or stone which they then used to produce the prints. These handmade plates would wear down as the edition was produced resulting in varying quality of prints within the edition. The first prints off the press would be the most accurate and detailed prints in the edition. These became known as "Artist's Proofs" and typically commanded a 30% or higher price for the higher quality images they carried.
Today, limited edition prints are virtually identical throughout the edition. However, the concept of artist's proofs still survive. Many artists still produce their own work and will set aside a portion of the limited edition to be sold as artist's proofs, mainly to art collectors. On the other hand, some artists get help producing and marketing their work from publishers. The publisher will usually reserve a percentage of the finished edition for artist's exclusive use. These artist's proofs can then only be obtained directly through the artist and are often sought after by collectors and those that wish to interact directly with the artist.
Artist proofs typically do not exceed 10% of the edition. Obviously, the fewer artist proofs produced, the more collectible they will become. They can be marked in the same manner as are the signed and numbered prints or they may have no number designation on them. All artist's proofs will bear the designation AP or A/P to mark them as artist's proofs.