A 'manual scram' is a scram of a nuclear reactor initiated by the operator. The operator hits a switch, turns a crank, or otherwise manually operates a system which re-inserts the control rods back into the core of the reactor, thus stopping fission and dropping power levels below critical. Cutting the rope holding a safety rod out of the core with an axe is a good example of a manual scram.
An automatic scram, on the other hand, happens when an automatic system triggers a scram because an instrument reading is out of the boundaries considered safe. For example, when the Reed Reactor Facility power levels go beyond 110%, there is a legal obligation for the circuts that read reactor power to initate a scram.
A manual scram can happen for any number of reasons, from an operator suddenly noticing aberrant readings on the control panel to wanting to impress a tour group with the decrease in the blue glow of Cerenkov radiation. It is also a lazy way to end an irradiation.