[Koshkin]

Since Vbe = const the transistor alone cannot amplify voltage. You need a resistor to convert the input voltage into current.

[fuzzfactor]

This is exactly it.

Your DC battery or power supply provides your headroom, and the transistor Base or Gate senses a small increment of that voltage and can sometimes deliver as much current as it takes to push the voltage across a resistance or impedance right up to the rails.