Since I can't post a thread due to my junior member status, here is the full breakdown + some theory filling in the gaps as to what MS has announced in regards to console operation so far.
Games have mandatory installation and can't be played off discs. Whenever a game disc is inserted and the game is not installed, an Xbox Live connection is required to initialize the install with a one-use key. On the first console you install the game on (main console that is associated with your account) the game will work for any user, and can be played without a disc in the console.
If the game disc is put in a console not mainly associated with your account, the game's install will be a limited one (where only your account is allowed to use it). If another user wants to play the game, they will be required to connect to Xbox Live and pay a fee (which is full price right now according to a statement). If the fee is paid, it becomes available to all users on the console.
Now for the second part. Everytime you log into your account, all the game licenses you have get activated for the console you're playing on (if this is your main console, it allows the game to be played by anyone, if it another, the license only applies to your account). This in turn sends out a deactivate license command to whichever other console had an active license for your games. So if that console happens to be connected to Xbox Live for a bit with whichever account, the games that are licensed to you will stop working right away.
Back to a console with an activated license. Once you disconnect from Xbox Live, a 24 hour timer starts on the game's license validity on that console. Once the license is up, you will be locked out of playing the game until you log back into Xbox Live with your account which will bring the licenses back to active status.
This is done by MS to prevent this type of scenario (with their game installation licenses):
Take a game like Skyrim which can take days if not weeks to complete and can be played completely offline for that amount of time.
Now User A has the license to Skyrim. He goes to User B and installs the game to Console B with his own account. Now User B disables the internet connection and plays Skyrim with User A's account for weeks on end, enjoying the game for free with no money spent on it while User A could also be playing Skyrim on his console while logged in online.
The only thing User B misses out on is achievements on his own account, but many people would not mind not getting achievements on their own account if they got to play games for free.
Anyways, with this 24 hour requirement. User B would only have a 24 hour period (rather than an infinite amount of time) to play Skyrim even while his Xbox was in complete offline mode and he was using User A's account offline.
Basically, pursuing disc-free operation has led to the creation of this crappy requirement.
Edit: And now I'm a member, LOL.