Adding a base resistor in a common emitter amplifier
A transistor amplifies current: you send current into the base-emitter junction, and an amplified current tries to flow in the collector-emitter junction. Current develops voltage when traversing resistors. So if you put a resistor down the emitter, the following happens:

when no current in the base flows, no current flows in the emitter too, so the voltage at the emitter is zero

you make current flow in the base, and the amplified current flows in the emitter. But the resistor raises the voltage of the emitter, so the voltage between base and emitter reduces, and less current enters the base.


It is a negative feedback, and this is why it stabilizes the amplifier.