A “decoder” is simply a piece of software that can do two things: decrypt the CSS encryption scheme used in DVDs and play back MPEG-2 video. In other words, DVD playback software.
Because both CSS and MPEG-2 are both tightly controlled, a DVD “decoder” will usually cost you money. Windows Media Player does NOT contain a decoder (it plays back DVDs through the use of whatever 3rd party decoder you have installed). WinDVD and Power DVD are the two most common ones. This is usually not a problem for people because manufacturers include copies of DVD playback software with their drive–and even OEM drives sold in bulk often get them bundled (in fact, because I’ve bought so many drives, I have way more copies of this stuff than I’ll ever need) (though that sometimes depends on whether or not the retailer is so generous). Did you get a copy with your drive? If so, did you install it?
I hear that Video LAN (google it up) can play back DVD videos (it’s freeware, and as you may imagine, it’s also under legal pressure, at least, that’s what I heard). I’ve never used it so I don’t know how well it works, but you could give it a try if you’re desperately seeking a free solution.