The MacBook / MacBook Pro needs a bit of power while sleeping, to keep its RAM running so it is useable immediately. So the battery will discharge. When the battery is close to empty, the MacBook / MacBook Pro will then store the contents of its RAM onto the hard drive instead of letting the battery run out completely and losing the RAM. When you start the MacBook again, it will then read the RAM back from the hard disk, which can take a while, but eventually it will be working as you left it. So if you wrote a document, didn't save it, put the Mac to sleep for a week, that document will be back when you use the Mac again.
(The new MacBook Air will do the same thing, but I think an hour after you put the MBA to sleep. From then on it will take very very little power to sleep, but waking up will take longer. That's why the MBA should be able to survive up to 30 days in sleep mode without power).
If your laptop battery is dead, you can still use the laptop with the charger plugged in for as long as you like. No problem at all. You will still have a small amount of battery charge, for example when the charger comes off by accident, it will still last for a bit. Do not remove the battery in that case.