It's to do with the characteristics of transistor operation. Transistors need about 0.6V between the base terminal and the emitter to turn them on.
So in the RIGHT hand circuit, Q1's base is connected to its emitter through the switch and R2, so there is no voltage between the base and emitter, and therefore the transistor is off. That means no current flows between collector and emitter. This allows R3 to pull up the base of Q2 - current flows from the positive supply, through R3, through the base of Q2 and out the emitter. This means the base voltage will be slightly above 0.6V, and Q2 turns on allowing current to flow through the collector and emitter, and through the lamp. Q2 is fully on and is said to be 'saturated', conceptually the collector and emitter now shorted together (with a small voltage drop - it's not a 'perfect' short, but assume it is for the moment).
The important thing to remember is that when one transistor is off, the other one is on.
In the left hand circuit, the operation is reversed. Q1 is turned on fully (saturated) because current flows through R1, through the switch, into the base and out the emitter causing the base-emitter voltage to be a bit higher than 0.6V turning it on fully. That means that the collector and emitter are 'shorted together'. Like the switch in the right hand circuit, this means that there can be no base-emitter voltage on Q2 because Q1 has essentially shorted Q2's base-emitter junction, so Q2 remains off and does not light the lamp. Current flows through R3 and Q1, but there's not enough voltage at Q2's base to turn it on.
There are some good examples here of the use of the weird parameters you'll see in the datasheet for any transistor. The 0.6V I keep mentioning is Vbe, and it varies hugely with temperature, voltage, current, time, all kinds of things. Current into the base of a transistor is Ib, the voltage drop across the emitter-collector terminals when the transistor is saturated is Vce(sat), and current through the collector-emitter junction (eg the current through the lamp) is Ic.