A manual transmission requires driver interaction to change gears, which also requires use of a clutch (with the exception of special situations). Because an engine has a limited range of RPM it can operate within (stalls out when too low, parts are working too hard when too high), a transmission is required to give a proper gear ratio for the engine to work with at any given speed.
A transmission is often titled a "(number)-gear transmission", and that number isn't a count of actual gears within the transmission (there are usually more than double that amount). That title tells you the number of forward speeds it has. Every "speed" is two connected physical gears,