Just like an engine, transmissions have a lot of parts that are under a lot of stress and would generate a lot of heat if not properly lubricated.
Automatic Transmission Fluid
Automatic transmissions and engines both need lubrication, but have different secondary requirements. Just like engine oils, automatic transmission fluid (ATF) has different grades.
Manual Transmission Fluid
Most manual transmissions are lubricated with gear oil, which is much thicker than oils used in engines, and usually contain fewer additives.