Twitter (!)... Can someone tell me what it is about and what people are looking for there?

[just "JR"]

I am developing a complex site that needs to access various social networks.
For this, I have to register with a great majority of these and find out how they work.
Not being a social network addict, I can't understand what people are looking for in these, but I am learning!
I am now analysing Twitter, and I really can't make head or tail of it!
I go to my page, and find a people "I follow", just to see multiple, irrelevant entries that have no meaning (except an obvious advertising trend).
So...
If you have a twitter account "well developed", I would like to follow you, to find out WHY I should "follow you"!
On the other hand, I would like to know what is your experience when you go on Twitter, and how does your "page" looks like!
If you are good enough with it, please, grab a screen image of what you are looking at and send it to me: I'll set-up an upload on http://www.jrcw3.com this afternoon.
Your comments on WHY and HOW you are using twitter would also be an invaluable feedback!
(I have seen so many questions here about twitter that I am REALLY puzzled!)