AT&T has always locked their cell phones - meaning, you could not use a non-AT&T SIM card in an AT&T phone without getting the phone "unlocked" (obtain a lock code from AT&T).
Verizon on the other hand has not locked its phones all for the last several years (per agreement with the FCC over licensing - long story). So you could pop in a SIM card from another carrier right after you bought your new Verizon phone.
Now Verizon has changed their policy: they will lock phones for the first 60 days of use after you buy them. After 60 days, the lock will automatically be removed, so no need to unlock.
So if you are going overseas and plan to buy a SIM card for your new Verizon phone, try to buy it at least 60 days before you leave on your trip. ;-)