Analyze Network Traffic

That's around the time that the nightly jobs run. Those kick off around 3 AM local time.

As for your question, here's a general intro of how to capture a packet trace, and you'll probably want to establish some sort of network monitoring on another host on your local network. There are some reasonable tcpdump primers available around the 'net, including one by Daniel Miessler, too.

I usually use a server-grade gateway-firewall for this sort of stuff (as well as a variety of other tasks), and most of these devices can minimally show you where the network connections are going; IP source and destination.

Really difficult to say without knowing a few more specifics - I'm tempted to side with Mr Hoffman and say it's either the local routines running or your backup - check your logs. If you have a spare machine around that can run a web server take a look at this http://www.ntop.org/products/ntop/