A "dog" is short for underdog, and represents the team or individual the bookmakers and lines makers believe will be the loser in a given competition.
The underdog is "given" points for bettors to take. The underdog only has to get within the point spread in order for someone to win the bet. The term underdog comes directly from dog racing and dog fighting (unfortunately, more the latter than the former). The expected loser of the fight or race was known as the underdog. Since a lot of gambling originated in dog and horse races, the term simply stuck to all sports gambling as the industry grew. In a typical betting line, the underdog will usually be listed with a plus sign and number next to it; this indicates how many points the side is being "given" by the bookmakers. In this example, the Los Angeles Lakers are the underdog: New York Knicks (-6) vs. LA Lakers (+6).