If you want to use the Kindle to read PDFs then the connectivity to the mobile network is not relevant once you have the PDF documents installed on the Kindle.
There are various ways documents reach a kindle, these include downloading them over WiFi and/or 3G connections. They can also be copied directly from a computer using a USB connection (using a USB cable to connect the kindle to the computer).
Here's more info, in case you are interested in knowing more about the 3G aspects...
3G is the main mobile network protocol available in many countries. Some kindles include 3G support, others may WiFi only, and some support both WiFi and 3G. A 3G connection uses a SIM card within the device, in this case a Kindle DX. Amazon use various SIM cards in their kindles. The main difference is which mobile / cell company they obtain the SIM card from.
AFAIK Kindles with 3G connectivity & sold in the USA have an AT+T SIM card installed. In some countries Amazon includes a SIM card from another company, Vodafone. The choice of SIM card can affect which countries the 3G Kindle works in. There is an interesting article on that topic, which compares the 2 configuration of Kindle 3 Keyboard devices.
Like you, I'm not quite sure why some sellers in the UK describe their Kindles as unlocked? Possibly it's to indicate that kindle might have a working connection abroad?