Emitter resistance in transistor bias
R1/2 fix a voltage on the base, which fixes a voltage on the emitter.

With a voltage fixed on the emitter, a known current flows through RE, through the emitter, and almost all of it in the collector.

Normally, a circuit like this would have a resistor in the collector lead as well, for this current to generate a voltage across. 

If the collector resistor was bigger than the emitter resistor, then the circuit would have voltage gain from base to collector. 

Sometimes the emitter resistor has a capacitor across it, so that the AC gain can be higher than the DC gain.