When you connect the emitter through a resistor, the collector to the
voltage source and apply enough voltage at the base for conduction, the
voltage across the emitter resistor will be roughly equal to the base
voltage minus the base emitter junction voltage (0.7v typical for
silicon transistors).
The voltage across the emitter resistor is independent of resistor
value, so it can be used to power high current drawing loads from a
small input current, since the current through the emitter resistor and
anything connected to it comes largely from the collector current
instead of base current.
This also isolates parts of a circuit from loading or otherwise
interfere with it's function. As such, they are also called voltage
buffers and impedance buffers
