How exactly does the switch work in a practical way? What is switching on under which conditions?

A switch could be acting just like a familiar circuit on-off switch - say, if $R_c$ at the collector were really a lamp's filament, you could turn on the lamp by setting $V_1$ high! Switches can turn blinky-lights on and off. Or anything on and off. The switch could enable activation or deactivation of different parts of a circuit, quite generally.

Another common usage is in digital logic: the ON and OFF states correspond to 0 and 1 bits, and you can make circuits out of transistors that perform computations. We'll see more of this in the last weeks of class.