"A claiming race in thoroughbred horse racing is one in which the horses are all for sale for more or less the same price (the 'claiming price') up until shortly before the race. Race types form a hierarchy in terms of the quality of horse they attract, with handicap races and graded stakes races attracting the 'best' horses and maiden races the most unseasoned. Claiming races fall at the bottom of this hierarchy, below maiden races, and make up the bulk of races run at most US tracks. For example in Kentucky in 1999, 54% of all races run were claiming races, but had only 20% of the purse dollar value, the lowest average purse among race types.
The mechanics of claiming vary based on jurisdiction but in most cases almost anyone, or possibly anyone who is licensed to own racehorses, may claim. For example, the Illinois Racing Board stipulates that any horse may be claimed for its entered price by any licensed owner or agent or anyone who has filed an application and been granted a claiming license. Title to the horse typically transfers just before the start of the race, but the previous owner is entitled to the purse, if any, that results from the horse's performance in the race. Usually related parties such as the trainer or employees, or relatives, are prohibited from claiming, as are reciprocal agreements between owners to 'protect' each other's horses. If a horse is purchased, a track official tags it (often with a red tag) after the race, and it goes to its new owner, assuming the new owner had sufficient funds on deposit.
Claiming races have claim amounts which vary, and higher amounts tend to have richer purses. The intent of this is to even the race; if a better-than-class horse is entered (with the expectation of an easy purse win), it might be lost for the claiming price, which is likely less than the horse is worth. Someone may wish to claim a horse if they think the horse has not been trained to its fullest potential under another trainer.
Claiming races serve several purposes. They are a quality classification, as well as a way of ensuring racing outcomes are less predictable, which in turn increases the handle, or amount of parimutuel betting, and a way to bring liquidity to the racehorse marketplace. Although many horses never rise above claiming races, some do. For example Stymie, a USD 1500 claimer, went on to earn over 900,000 USD, winning many storied grade 1 stakes and handicap races in the 1940s. General Quarters, a USD 20,000 claimer, won the grade 1 Blue Grass Stakes and ran in the 2009 Kentucky Derby. Make A Stand, claimed for £8,000 in 1995, won the 1997 Champion Hurdle."
"...not all horses are good enough to be top competitors in stakes level races. Claiming races are the great equalizer; basically the owner is setting the market value of the horse. If the horse is entered for a price that other trainers think is a good value, it is likely to be claimed. Conversely, if he is entered for too much, the horse often ends up being a long shot and having a slim chance of winning. Depending on the track, a horse may be entered anywhere from $5,000 to as high as $150,000. There is also another type of race called the optional claiming/allowance; a type of hybrid race that combines claiming horses with those still eligible for allowance conditions. In this case, the horses may be eligible to be claimed or they may be running for allowance conditions, and therefore are not eligible to be claimed. This type of race helps the Racing Secretary have a fuller field of horses and gives trainers a couple of options when their desired race does not fill when entries are taken." Horse Betting: Claiming Races