How did my water meter become loose?
The meter likely has rubber gaskets that make a seal between the meter body and the pipes; like a garden hose.   Temperature changes or age (likely only if the city installed a used meter with used gaskets) could have changed the pliability of the gaskets. I can't say if the nuts loosened, but there shouldn't be any teflon tape or pipe dope on the threads.  If they start to leak again, or if you're sufficiently worried, you can check the gaskets. Turn off the water at the main and you can easily take the pipes apart from the meter and inspect the gaskets.  New ones can be purchased at any plumbing supply store for a couple bucks.