I just don't understand it.
The few times I have clicked on a link it seems to take me to some other topic.
Then when you do get to a topic it just seems to be people saying @ so and so over and over and there never appears to be anything said / written.
What is all about?
Sounds like you may be using it a bit clumsily, you should get to see a thread with replies rather than "@" with nothing else, although I vaguely recall seeing similar when I first tried it. I think you're seeing people calling others in to a thread, but you're not seeing the thread itself.
Try this: From your home page (bird house symbol), click on the search button (magnifying glass icon) then click the trending topic tab at the top. Then there will at least be plenty of replies to the most popular tweets for you to see / play with / start a fight with.
Then if you click on say, Nat Phillips, you get a whole raft of tweets, but look for those that have the most replies in order to get your maximum reading entertainment, enlightenment, or fights.
The one above has 106 replies which suggests some fruity discussions are going on. Click on lfcandreas's text, and it opens the thread and shows replies. You may join in by clicking the blue feather if you have a constructive input. Or indeed if you don’t have anything constructive, but just want to flame... it's not compulsory to be pleasant and reasoned on Twitter.
You can do the same search for any topics or key words. Don't bother posting new threads if you're someone with 12 followers.
Have fun with it!
Personally I think it's a limited and poor medium which discourages proper debate and instead encourages polarised soundbites, but it can be fun in small doses so long as you don't get too sucked in.