If the material is distributed under conditions which are explicitly forbidden by copyright or other legal conditions, yes.
So, in the vast majority of cases, yes.
Material in the public domain or copyrighted material which permits free distribution (e.g. software under the GNU GPL for example) can be torrented legally.
As for why it is illegal, it should be obvious. Copyright infringement is illegal.
BitTorrent is just a protocol. It makes no difference as to whether or not you infringe copyright by using torrents or by using Rapidshare or by buying an unauthorised copy off the street or get a copy from a friend. BitTorrent in and of itself is not illegal, but it can be used for illegal purposes.
Somewhat like a kitchen knife. Kitchen knives aren't illegal. You can chop cucumber and carrots up for a salad with a kitchen knife and it's legal. Stabbing someone randomly with it or hold up a store, and it's illegal. In either case, it's not the kitchen knife that's illegal, it's the act of randomly stabbing someone or holding up a store.
Asking whether BitTorrent is illegal is really asking the wrong question. The question should be: 'Is copyright infringement illegal?' The answer is obvious—yes.