Carriers test devices. This testing is for new devices and for software updates and not all devices are subject to the tests: some Nexus handsets and anything with an Apple logo receive their updates directly from the manufacturer and so are not always tested. Depending on the device and carrier, sometimes these tests can take many man hours to complete: carriers can and do vary their testing depending on their history and experience with a particular device manufacturer together with the severity of the changes in any particular update. And these tests are not simply a formality: at the time, the carrier or manufacturer usually won't admit it but it happens. O2's original launch of the Sony Xperia Arc was delayed because the device failed Telefonica's tests, and subsequently when it came to the upgrade to Android 4.0 Ice Cream Sandwich, the device ahead again failed and was never officially updated.
To get specific about Verizon Wireless, their reputation within the industry is that they take extra time to approve and release updates. This is something many of the more mobile-aware customers find frustrating, especially when their buddies on different networks received a given update months ago! Verizon also run a number of tests on devices designed to check on a whole number of things including durability, signal attenuation, call quality, battery life, software functionality. In this respect they are little different to the other carriers and it is difficult to measure how much deeper their testing! Now, Verizon are taking us through some of their testing through a YouTube series called "The Device Lab."
Some people have questioned the need for the carrier to test the device in presumably a similar way to the manufacturer. The answer is simple: Verizon need to be aware of particular issues that its customers might encounter so as to be better prepared to support them. And let's not forget that the carrier store is the first place that many people take their troublesome device to, where it may ultimately be sent to their repair centre, because the customer's contract is with the carrier. And finally, the device that you buy from Verizon is subtly different from the device you might buy from the carrier and in order to ensure that it works properly, if Verizon are going to put their name on it, they are going to check it. Perhaps the more Verizon badges the device wears, the more in-depth the testing..? Check out this one example clip below.