Rem is the Shinigami who first gives Misa her Death Note and Shinigami eyes. Similar to Ryuk, Rem possesses two Death Notes; she purposely gives a Death Note to Misa. Rem inherited her second Death Note from Jealous, another Shinigami who died when he saved Misa's life, and thought it only right to pass it on to Misa. Rem inherits Jealous' love for Misa as well and is prompt to defend Misa even at the cost of her life. She shows this when she openly shows her lack of trust for Light stating that if Misa dies before her time, Rem will kill Light. In the manga and anime, Rem tells Misa that she is actually a female Shinigami. In the second live-action film, this is not mentioned, leaving it ambiguous.

(Source: Wikipedia)