First of all, what is a Verizon iPhone and what is the difference between the Verizon iPhone and non-Verizon iPhone (e.g. AT&T, your local mobile providers)?
Verizon is one of the largest mobile carriers in the US. Verizon iPhone 4 means that the phone is powered by Verizon. Basically, the main diff between the two iPhone 4 brothers is the network technology. For more technical rationale and explanation, you can refer to this site.
If you're not living in the US, it's not really recomended to get this phone. To make the Verizon iPhone international it would have to have a GSM chip and a CDMA chip. The rest of the world runs on GSM, while Verizon uses CDMA. The CDMA version of iPhone 4 is configured to work only with the wireless services of Verizon Wireless. Therefore, you can only use the phone in selected countries (now 40) which support CDMA technology and Verizon Wireless as it can only run on Verizon Wireless’ 3G network and not in any other 3G or 4G LTE networks.
So if you find iPhones cheaper from the US in eBay or other similar sites, just consider buying an AT&T phone even if it's locked. You can insert your local SIM to an AT&T iPhone and jailbreak the device to unlock, whereas this is not possible using a Verizon iPhone because it doesn't cover a SIM-card slot. Or better yet...iPhone 5, anyone? :D