Historically, artist's proofs were proofs pulled from production so the artist could check the quality of the print. Because they were pulled early in the production process, they often contained more vivid colors and lines and were considered more valuable. The proofs were often given to the artist as payment for signing the rest of the edition.
Modern printing technology makes all prints equal in quality, so today's artists are given 5 to 10 percent of the entire edition for their personal use, as part of their contract with the printer. Sometimes the printer is also allowed to keep some of the artist's proofs.
Artist's proofs have always been considered more valuable than a print from the regular edition, because they have been part of the artist's personal collection.
Artist's proofs can be identified by an "A/P" on the print, usually in the bottom-left corner. It may be accompanied by a number, if the proofs were numbered separately from the rest of the edition. It should also be signed by the artist.
An artist's proof and a limited edition print are not the same thing. A limited edition print is a numbered print from a predetermined number of a particular print. The artist's proofs are separate from the numbered prints.