As long as the transistor is in just the right state (R must be adjusted to give this "right state") then the output voltage variations are much bigger than the input voltage variations. The input voltage is the voltage across points A and B and the output voltage is the voltage across the collector and emitter of the transistor.

The "wavy lines" on the diagram represent what would be seen on an oscilloscope screen when the circuit is operating correctly. This shows why we call the circuit an amplifier: to amplify means to make bigger.

The resistor, R_b, is called the base bias resistor, and the very small current which flows through it is called the (base) bias current.