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!)
"You can meet celebrities and write to them, and they might reply"... Interesting.
Does that mean that the reply will appear on "your" page?

If you don't mind, give me your "details" (or whatever I need), so I can "follow you"... :-)

Eli: I won't have the patience to "experiment"... :-) That site is pure "cr*p" !