So the reason why Verizon uses SIM cards is because LTE is a GSM technology and GSM requires the use of SIM cards. Currently, only data/SMS/MMS is transferred over the LTE network while phone calls use the CDMA network. So when you transfer to a new phone, you have to take your SIM card to the new phone otherwise LTE data will not work (3G will work when you flash over). Because your wife is moving from an iPhone 4 to iPhone 5, you will need to go to a Verizon store and tell them that she needs a new SIM card for her phone so that LTE data can start working. Otherwise, your wife will be stuck with 3G data once she flashes over to iPhone 5.
In the future when verizon activates VoLTE (4G voice), they will be shutting down the CDMA network to have all data/voice/messaging over 4G/future 5G networks. Flashing will no longer be required, and only SIM cards will be used to identify users, just like GSM of today like at&t/T-Mobile. You can think of Verizon being in a "transition" phase from a CDMA carrier to a GSM carrier. With VoLTE coming online sometime next year on Verizon, your iPhone 6 may as well never connect to the CDMA network again as it will no longer need to fall back to CDMA to make phone calls.