Most specifically, irrationality means that rational systems are unreasonable systems. By that I mean that they deny the basic humanity, the human reason, of the people who work within or are served by them.
I tend to be a loner I think a lot of social theorists are like that. On one level, the majority of the most important people to me are people who I have imaginary conversations with in the deep of the night: I'm often in conversation with Max Weber or Karl Marx or someone like that. Those are the people I'm closest to and that have had the most influence on me!
Coca-Cola is little more than sugar, some flavoring, and lots of (carbonated) water. It is largely indistinguishable from innumerable other brands of cola, yet people around the world seem to think that Coca-Cola is something and they are eager to ask for it by name and even to pay a premium for it.
What defines Web 2.0 is the fact that the material on it is generated by the users (consumers) rather than the producers of the system. Thus, those who operate on Web 2.0 can be called prosumers because they simultaneously produce what they consume such as the interaction on Facebook and the entries on Wikipedia.