The definition you have mentioned is possibly correct in one sense.
Actually an active device is a device that seem to be supplying power on it's own.
For example you take the case with transistors. They doesn't produce any power on their own. But, they can be visualised as a constant current sources. They simply utilise the power from the biasing battery and they supply it to the loads. Where as a resistor cannot do that. Hence resistors, capacitors and inductors are passive devices.A diode can rightly be called an active component.
It is nearly always a source of emf, but its important property could be that it is sending a signal of some kind.
where as a passive deviceis a device incapable of current gain or switching, such as a resistor or capacitor.
Think of transistor, it will have a current gain.
For instance think of a resistor, it's state does not change after you connect a power supply. But, for a diode or a transistor lot many changes take place in their states after the connection of a source in the circuit. Moreover their states also depend on the way in which they are biased(connected to the sources).