Before I start into my de-myth'ing explanation/rant, realize that I understand you are unaware of the nature of torrents. So if at any time, it seems as if I am directing the comments at you, realize that my commentary is aimed at those who understand the technology but still choose to defame it. (Or worse, choose to rally against it, knowing nothing about it, save propaganda from anti-torrent organizations.)
Ready? Okay, here we go....
A torrent is a way to connect multiple computers by way of a decentralized method, in order to share files piecemeal.
Compare this to a centralized method, where a computer hosts a file and then your computer connects to it and downloads the file. For example, you go to adobe.com and download a trial of Photoshop. Your computer connects to the Adobe computer with the file, and it is transferred.
Now, that carries a big cost to Adobe, who must pass along a large 1GB or so file, sequentially, one piece at a time. They have to pay for all of the bandwidth outbound, it ties up their computers, and it's a relatively slow and linear transfer process. FTP is the same.
With a torrent, many computers share piece of data between one another. This both offloads the bandwidth costs and can speed up the transfer, as you're connecting to many computers at one time instead of just one.
The controller here is the ".torrent" file associated with the desired download. These files are centralized on a server, and are not wholly different from a search engine. Google, for example, looks at what computers have which web pages (which are essentially still just data), and then makes a public index. Torrent "trackers" monitor which computers have certain files available, and then publish the .torrent files that enable the connections between all available systems with that file. Much like search engines, trackers update their information on their own schedule (hours, days, etc). All computers involved in downloading the file, or the "seeds" (computers with finished downloads and still online), broadcast their availability by being connected to the torrent. You can't really download without also being an uploader, with the rare exception that you're downloading something that nobody else seems to want at that moment (and you're simply downloading from a seed). Since I'm defining terminology already, I'll add that a "peer" is another computer that is uploading/downloading a file, but does not yet have the complete file (and is therefore not yet a seed).
Now, like anything else, technology can be used for nefarious reasons. Illegal copies of full versions of programs, cracks/serials, MP3 files, in-theatre movies, etc. But you could do the same thing with email (send an MP3 to a buddy), an FTP (download full version software), "file sharing" services like Rapidshare, or even underground web pages. But various industries have chosen to rail against the technology, rather than use it or try to understand it.
Attempting to insinuate that "torrents are illegal" is asinine, yet many people have fallen for this horsecrap because they don't understand what it is (and sometimes don't seem to care to put forth any effort to understand it). So kudos to you for not believing the BS and trying to learn what it's all about.
When the "it's illegal" angle failed, the fall-back plan is to somehow make it out to be a hotbed for viruses and malicious software. I'm sorry, but that's equally as idiotic as the legality point. If anything, email still proves itself to be one of the worst places to acquire a virus, followed by websites for malware. I've never seen a torrent virus -- although I'm also not trying to download illegal software (I prefer to buy my software, thanks much).
Indeed, many techs and artists alike have adopted the torrent system, because it reduces their costs. Right now, the counter to propaganda is to outright release content on a torrent, which earns many of these folks instant media recognition for their so-called rebellious act. Entire DVDs can be downloaded quickly and easily (assuming enough seeds and peers are active), be it an indy movie or a Linux OS installer, as an ISO file ready to burn with the freeware
ImgBurn.
I have 2-3 movies from this summer that I've not had time to watch -- indy flicks released exclusively on torrents, because the creators lacked the funds to create elaborate sites with costly downloads. It also allows them to distribute higher quality versions, in a format people like (DVD), instead of forcing them to watch a watered-down quality version on Youtube or Vimeo (and likely in smaller chunks, given the time limits on those services).
As to your specific example on finding three movies/specials, and seeing VHS copies on eBay -- I won't comment, and I really don't want to know any more information. That sounds a little gray area to me. But then again, giving the benefit of the doubt, those could very well be the types of official torrent releases I've seen in the past. I do know that at least one of them provided torrents for free, but charged for DVDs (or VHS tapes) if anybody wanted to buy them. Being the supportive guy I am, I actually bought the DVD so I could get the DVD case artwork and an autograph -- you never know when he may become famous!
In some countries, there are legal exceptions that allow for the use of torrents to act as the "timeshifting" devices for watching TV shows. Of course, even in countries where certain groups insist the activity is illegal, there's technically not any law or statute explicitedly stating it -- thereby creating a lot of legal gray areas that are still not tested in the courts of that locale. I don't know all the specifics, and I'd prefer not to comment further, as that becomes a bit off-topic for this discussion.
For the best torrent software, I highly suggest Vuze (formerly known as Azureus). When installing software of any kind, including this one, remember to not just blindly click "yes" to everything -- read what it's doing. Uncheck options to install unwanted crap, like toolbars and virus scanners -- just install the software you downloaded and nothing more.
What you'll do is visit a tracker site, and then either download the .torrent file (and then double-click on it to launch your torrent "client" software), or simply click on the link in your web browser and the browser will auto-launch the torrent client. For example, Firefox will launch the client, while Chrome will not (at least not on my system).
It's really not much harder than email, FTP or even jumping through the hoops required to use most software. Don't be scared away from using this excellent next-gen technology.
If anything, the distributed computing method is the future. For example, where websites once used dedicated computers (or a network of dedicated computers) to power the site, distribution across a "cloud" of computers can run a site both faster and safer, spreading the content and tasks across multiple networked system. Torrenting was one of the first widely-used methods to distribute information in a decentralized method, and it certainly will not be the last (or even the latest, seeing how "cloud computing" is now the in thing).
I hope that clears up the misinformation, myths and bogeymen you've heard in the past.