They say AT&T or Verizon because there are two different mobile networks in the U.S., GSM and CDMA. AT&T (and T-Mobile) use GSM. Verizon (and Sprint) use CDMA. Phones made for one network will not work on the other. If you want an unlocked phone that you can use outside the U.S., make sure you get one that will work on the network that country uses. Looks like GSM for Israel--also for Europe, not sure about other places.