In the United States, most all carriers require you wait a certain amount of time after buying a phone before you can use it on another network. It's a process called "locking", and it's something that's instituted by AT&T, Sprint, and T-Mobile. Beginning at some point this spring, Verizon will follow suit.
With Verizon's current policy of selling unlocked phones, you can purchase any device from the carrier and instantly start using it on another network that supports it. It makes it easy for consumers to take their devices to other providers as they see fit, but according to Verizon, it also makes it easier for crooks to steal these devices and sell them on the black market.
Verizon's following the industry norm.
Once Verizon changes this, you'll need to wait for an undisclosed amount of time after buying a phone before taking it somewhere else. The carrier hasn't said how long this waiting period will be, but if its similar to what we already have, we'll likely be looking at anywhere from 15 - 60 days.
I don't buy into the idea that something like this helps to cut down on theft, and instead feel that Verizon is making this change as a way to deter customers from buying its phones and using them on a competitor's network. It can certainly be seen as a hostile act towards consumers, but from a business point-of-view, it makes sense for Verizon. The rest of the industry already does this, and if it can keep more people on its network in the process, it might as well.
There's no timeframe as to when these changes will be made aside from "this spring", so if you were planning on buying a Verizon phone and using it elsewhere, I'd suggest doing so soon before this goes into effect.