Emitter Follower as a Current Amplifier
The Emitter Follower's Input/Output impedances however show totally
  contrasting properties (High Input and Low Output impedance), and from
  small signal models its quite easy to see that the Emitter Follower
  does provide a significant current gain (β+1)


You need to do a small-signal analysis of the input impedance for signals above the base-emitter diode voltage (~.6 volts). In this regime, you'll see that a small increase in voltage will produce a large current increase, which is the mark of a low impedance.

Likewise, if you hold the base current constant, you'll see that the emitter current does not vary much for variations in load resistance. And this is a mark of high output impedance. Granted, for a single transistor it's not outrageously good, since beta varies with current and collector-emitter voltage.