Keith's explanation was technically quite correct, but you may have been looking for something a tad more basic and practical. It just means that the collector of an output transistor is literally not connected to anything internal other than the pin itself.
No, thats "open collector". We are talking about the common-collector configuration (I assume), almost always called
an "emitter follower" BTW.
The voltage gain is about 1 (well very very slightly less than 1), current gain as explained above. The normal reason
for this circuit is to take a high impedance signal and generate a low impedance output. Its (small signal) output
impedance can be much lower than the emitter resistor, note. The large signal behaviour is very asymmetric
which can be an issue.