Transistor terminal impedence?
It's the impedance seen at each of the respective terminals. 

It is important as it can be used to advantage in e.g. current amplification (base high impedance, emitter low impedance)  

Or a (non ideal) current source (collector high impedance)    

Voltage (and current) amplification (base high impedance, collector high impedance with resistor for current to voltage conversion or "transresistance")

The above is just my (probably not so great) attempt at a rough picture and is by no means the full story - any decent book on electronics should discuss the various uses of common emitter, common base, common collector amplifiers and their in/out impedance relationships and current/voltage gain. You can see how each makes use of the transistors characteristics if you study the associated theory.