To be excessively technical (you tuners know what I'm on about):
Manual allows you to change gear at any given moment, and any RPM within the rev range(idle-rev limiter), which gives you the freedom to shift to the proper gear at an appropriate time.
For some cars, this is absolutely necessary; If you look at the power/torque curve(garage>car>tuning>green and orange lines on right) the curve is like a cone, where it peaks at one point
in the middle, and it drops after that peak. It means after a certain rev, the engine cannot produce more power, and will drop in power the further on you go in that gear. If you shift just after that point, you will be using all of the power the engine can give. That is only possible in a manual.
In an automatic, the game shifts at a preset RPM, usually near the redline. For cars that have a cone-shaped power/torque curve, this means that it will shift once all of the power in that gear is gone
