A spin-off in television is a new series which contains either characters, a different character or theme elements from a previous series. They are particularly common in situation comedy. A related phenomenon, not to be confused with the spin-off, is the crossover.
Many, if not all spinoffs, are produced by some of the original producers of the root show.
A revival series, a later remake of a pre-existing show, is not a spin-off (e.g. The Battlestar Galactica series of 2003 is a revival, not a spin-off of the 1978 version). An exception can be made to series such as The Transformers where the lines of continuity are blurred. If a television pilot was written but never shot, it is not considered a spin-off. When a show undergoes a name change, it's considered as the same show.
Neither is a reboot series, a term recently invented for motion pictures, which can also occur in television. This is distinct from a revival in that there is little or no attempt to retain continuity with the original. A recent example is the 1987 series Beauty and the Beast, rebooted as the 2012 Beauty & the Beast, which keeps only the main premise of a female law enforcement official aided by a man-beast, the New York City locale, and the names of the two main characters.
Some spin-offs are "engineered" to introduce a character to one show, just so that that character can anchor a new show (that episode of the original show is often known as a "backdoor pilot"). For example, the character Horatio Caine appeared on one episode of the Las Vegas-based CSI: Crime Scene Investigation before the premiere of CSI: Miami. Shows such as Enterprise, What I Like About You, and Deadline which have no immediate connection to previous series but are still known to exist within the same fictional sphere are also spin-offs.