Here's what I think is a good way in to the core metaphorical meaning of the verb 'stagger' (in the sense that you're looking at in the dictionary).
Imagine you're the organiser of the Berlin Marathon. Every year, there are 50,000 people who want to take part. Now, it would be very problematic to let everybody start running all at the same time with a single starting time, right? If you start the race at 9.00 am, you're going to have serious problems of congestion, what with 50,000 people all running through the streets at the same time. So what's the solution?