Interactivity is nothing new. People have been interacting for as long as they've existed. What is new is that we consider it possible for computers to be interactive, that is, for people to truly interact with computers and related technologies, rather than just use them.
Interactivity is not a definable thing so much as a nebulous concept. It is a spectrum from passive to interactive and there's no distinct point along the spectrum where an experience switches from passive to interactive. In fact, it's probably only possible to compare experiences as being more or less interactive than each other rather than interactive in and of themselves.
In an interactive medium, it would seem that interactivity would be important, but the issues over the last few years have revolved around most everything but interaction: content, technology, bandwidth, connectivity, politics, security, etc. Even those who claim to understand interaction usually produce merely dynamic media (such as animation) instead of interactive experiences. Interactivity is the differentiable advantage of interactive media. We have had multimedia for a long time (in print, television, etc.) but what is different now is interactivity. Technologies are not inherently or automatically interactive. They must be made so through careful develop that makes a place for the audience (users) to take part in the action. Products and experiences in these media that aren't truly interactive (for example, those who merely use the medium to broadcast content or recreate traditional passive media experiences like television), won't be successful because they aren't using these media to their advantage. Television will always be better at being television the Web or other interactive media.
The biggest problem with the term interactive is that it has been misdefined by too many companies and people as meaning either animation (which is an old passive medium) or anything that appears on a computer or on the Web since these are "interactive media." Unfortunately, these definitions are not only incorrect but misguided in how narrowly they look at activities. Interactivity encompasses everything that we do, not just do on or with computers. In fact, most interactive experiences in our lives have nothing to do with technology. Playing sports or other games, hobbies, and work are more interactive than computers have been able to address. Probably the most interactive experiences in your life will be great conversations.
What's important to understand is that everyone already creates interactions for themselves and others, we just don't think about it. However, we already know a great deal about interactivity from which we can draw experience, processes, and techniques for creating computer-based interactivity.
Interactivity is also comprised of many other attributes. Some of these attributes include: feedback, control, creativity, adaptivity, communications, etc. Many of these are also valuable experiences for people (certainly creativity and productivity) and, correspondingly, interactive experiences that take contain these are highly valued when design well. Interactivity isn't necessarily better but it does, usually, correspond higher involvement by an audience.
On a philosophical level, interaction is a process of continual action and reaction between to parties (whether living or machine). It is probably debatable whether or not a computer is capable of actually initiating action instead of merely reacting at all times through its programming. This may be one of the key differences between animals and machines and may lead us to design more interactive experiences.