In the jargon of Zombie Squad and other survivalist groups, to bug in is to hunker down at a secure location until a situation improves. It contrasts with "bug out", which means what it does in Army parlance - to leave a place with haste.
The first decision a would-be survivor makes when a crisis strikes is whether to bug out, or to bug in. It makes sense to bug out if you have a clear way to do so and a secure location to go to. A bug out bag contains the essentials needed when bugging out. If you don't have one and can't get it in one hell of a hurry, it's probably better to bug in. There are always exceptions, of course - it's probably not a good idea to bug in if you're expecting a tsunami - but the idea holds. If you're not prepared to run, you probably stand to make things worse by doing so; hence, why you should bug in.