To bug out, in military parlance, is to leave or evacuate an area. One bugs out when resistance is too heavy or when a position otherwise becomes untenable. Survivalists use the term in much the same way. Bugging out is what one one does when faced with a crisis, and bugging in is not a viable option.
A bug out bag is the bare minimum you should have with you when bugging out, but don't carry too much. If you think a crisis might require you to bug out, it's best to do it before the government issues a directive to evacuate, if you can. That way, you get out before the roads become clogged, and you have more choice about where to go. Just ask any of the people who fled from hurricane Katrina why this is important...