Spin-off is the act of creating a company from a division of a larger parent company.
A spin-off is sort of like a reverse merger. A parent company separates a division of itself and sets it up as an independently operating and independently trading company. Usually, shareholders of the parent company receive shares of the newly formed company.
Sometimes, companies wish to "unlock" the value of a division, believing that the market will more correctly value that division if it operates as an independent company. If they are right, then shareholders will benefit as the total value of the two independent companies increases.