Dealer's Choice is a method of determining which variant of poker to play. As implied by the name, the variant selected is usually the choice of the player who is designated as the dealer, though it can be done by majority vote or other selection method. The key is that the decision is not made by external management, but by the players at the game themselves.
Dealer's Choice is frequently found in home games, but can occasionally be found in a casino as well. In particular, smaller casinos that cater to a small group of regulars tend to behave more like home games, and will sometimes officially offer Dealer's Choice tables (such as at the Ocean View Card Room) or tables which are effectively, if not officially, Dealer's Choice (such as at the Lucky Buck Card Club).
From a practical standpoint, most Dealer's Choice games play a full orbit of a particular variant prior to selecting a new one. This eliminates the problems of different dealers switching between games where position is important (e.g. Hold 'em) and those where it is not (e.g. 7-Stud), potentially always disadvantaging a player in a bad position. As an example, imagine sitting two seats to the left of the only player at the table who wants to play Hold 'em, while everyone else wants to play stud. You would always be stuck with the big blind, while no other player would ever have to pay one. This seems unfair, and leads to Dealer's Choice games sticking with a particular variant for a full orbit before switching.
Technically, HORSE is not a Dealer's Choice game since the games are declared in advance of play, but it often behaves like one. Players also often alter the game to their liking at the table, by adding other variants if they desire (e.g. adding Badougi to a HOSE game).