Quick questions on The transistor as an amplifier explained: O-Level Electronics Amplifiers

A transistor amplifies because a small base current controls a much larger collector current, related by the current gain $\beta = I_C / I_B$. When a small signal changes the base current slightly, the collector current changes by $\beta$ times as much. This current amplification is the starting point for making a transistor amplifier.

To get an output voltage, a load resistor (the collector resistor) is placed between the collector and the supply. The collector current flows through this resistor, so by Ohm's law the voltage across it depends on the current. When the collector current changes, the voltage across the resistor changes a lot, and so the collector voltage swings by a large amount. This swinging collector voltage is the amplified output: a large copy of the small input.

Voltage amplification means the output voltage signal is larger than the input voltage signal. The voltage gain is the ratio of the change in output voltage to the change in input voltage. A single common-emitter transistor stage can give a useful voltage gain because a small base voltage change produces a large collector voltage change. The output is also inverted: as the input rises, the collector voltage falls.