There could be a few reasons why it's not opening - first, the DVD drive itself could be faulty. Maybe it's a power- or motor-related issue, and it won't work until it's fixed. Another option is that there could be a disc (or more) jammed inside and it won't open.
I took a search for this and came up with a few results, and hopefully some help for you. This one is directly from Xbox Support, and shows you how to manually eject your Xbox 360 optical disc tray.
The one below is from YouTube, and shows you how to open up a stuck Xbox 360 DVD drive.
If these methods don't work, try a console repair shop.