Transistor action, transistor as an amplifier
The current gain of a bipolar junction transistor (BJT) (one that has a collector, base and emitter) is the ratio of collector current (Ic) to base current (Ib) when it's not saturated. For most BJTs, it varies sufficiently slowly with current that it's worth giving it the name 'current gain'. It is also called beta, and hFE. 

For typical BJTs, the beta is substantially constant (within a factor of 2 or so) over a large range of Ic from around 0.1% to 10% of rated Ic, in other words the useful or intended operating range of any given transistor. It tends to fall quickly in the top decade of rated Ic. There is also a strong temperature dependence of beta on the device temperature.