In Common Emitter Amplifier Circuit ,Emitter Capacitor effect
In a common emitter amplifier with an emitter resistor the collector current and the emitter current are almost identical. 

"Gain" is proportional to collector voltage / emitter voltage (by definition) so as Vc = Ic x Rc and as Ve = Ie x Rc and as Ic ~= Ie, Gain = Rc/Re.
 Rc = collectpr resistor and Re = EFFECTIVE emitter resistance. This is the transistor internal Re_internal + theemitter resistor.

If there is no emitter capacitor across the emitter resistor then
 Gain = Rc / (Re + Re_internal).
 If the emitter resistor has a capacitor across it which allows AC to pass with no loss (or not much loss) then
 Gain ~= Rc/Re_internal.  

Re external is used to set the DC operating conditions and maximum AC gain occurs when the only emitter resistance = Re_internal.

For a silicon transistor Re_internal "just happens" to be 26/I ohms where I is the emmitter current in mA. This is a basic property of the silicon junction which I'll not go into further here. It makes sense when examined but is not intuitive. 

ie if i=1 mA then Re_internal = 26 Ohms.
 If Ie = 4 mA the Re_internal = 26/4 = 6.5 Ohms
 If Ie = 10 mA then Re_internal = 2.6 Ohms

SO for a fully AC-bypassed Re  (large enough Ce) :


Gain = Rc / Re_internal = Rc / (26/mA) 
Following this through you arrive at the "fact" that
Gain = 38.4 x Vc
Not many people know that.
Few people believe it when told :-)