The meaning has been broadened through popular use and, in so doing, it has become diluted by people who either don't apply it properly, or seek to draw parallels which get mistaken for genuine associations as time passes. That's what popular culture does - I wince whenever I hear or read news about "hacking" which invariably demonstrates a complete lack of insight into what was perpetrated.
My degree was in Biomedical Engineering and Cybernetics. The etymology of cybyernetics has already correctly been given here as κυβερνητικός (kubernētikós), the Greek sailor exerting control over his environment, and that is the true meaning of the field. It is about intelligent systems of control, nothing more, and the essence of this is a very simple concept: feedback. Like the Greek sailor, it is not enough to exert force to achieve will - the results of the exertion must be perceived, and compared with the desired outcome. If the sailor finds he is veering to the right due to winds or currents, he must apply change using the rudder in order to maintain his course. Thus his actions in this instant are predicated on the results of his actions in the preceding instant(s); what is happening influences what will happen next.
Taking an example of technology, consider climate control within a building. Once the thermostat has been set, the system has been given its desired outcome: say 26 degrees Centigrade. If a room's temperature exceeds this, then the air conditioning will be triggered and the room will be actively cooled, until the point at which the desired temperature is reached, when the system will cease running the aircon. Conversely if the room is too cool, heating will be engaged in the same manner. We're all familiar with this form of feedback, and any system which incorporates it may be thought of as cybernetic, although it is generally only applied to systems created by humans.
The reason cyber has been applied so universally to mean all things internet-enabled is not because of the internet itself, but because of the properties of this system. I can say something to my friend while he is standing next to me, or I can write my message down on a piece of paper and show it to him - the outcome is the same (leaving out the lack of body language/intonation which is a subject for another discussion). The outcome remains the same if I type it on an electronic device, and show him the screen. It still remains the same if I type it on an electronic device and it appears on the screen of his electronic device - but now, the properties of the conversation have altered. The same message is conveyed, but (i) I no longer need to be next to him, so long as we are connected to the same infrastructure, and (ii) I don't have to be giving my message at the same time as he is able to receive it. Our communication paradigm has been decoupled in both space (we are telecommunicating, from the Greek τῆλε meaning afar, far away) and time (we are communicating asynchronously, from the Greek σύν (sún, “with”) + χρόνος (khrónos, “time”), negated with a).
However, this decoupling is not to be confused with cybernetics. If we ignore all of the cybernetic systems that facilitate the actual internet, as parts of the infrastructure, then it becomes clear that use of the internet as a medium does not constitute a cybernetic system in itself. The outcome of me delivering a message and my audience receiving it is the same, whether I am standing on a podium in front of them or posting it on my Facebook page. The internet simply becomes a tool, a mechanism used to perform this action remotely and asynchronously; the fact that it utilises cybernetic principles does not make any system that involves it inherently cybernetic per se. If I follow someone down the road and hurl abuse at them, I am bullying. If I do it on Facebook, I am bullying. The fact that I did so using a different medium does not change the outcome, and words like "cyberbullying" are part of the reason why our legal system has been so insufficient and outmoded in tackling all of the issues that are arising from an internet-enabled world, such as online abuse and so-called piracy.
TL;DR: words like cyberspace, cybercafe and cyberterrorism all refer to the same thing as their real-world counterparts, which are taking place by leveraging (usually internet) technology. The conflation of this medium with the basic action itself does not alter the meaning of the word. In this context cyber, by itself, has no inherent meaning, in the same way that "app" is short for "application" and nothing more.