3G is a mobile-phone network capable of respectable data-transfer rates. Coverage throughout Europe is generally very good, but will obviously vary a little from network to network. More here - http://en.wikipedia.org/wiki/3G_network
I don't have a Kindle or know anyone who does, so the following is based on what I've read:-
Kindle 2 'International' edition restricts 3G access to the Kindle bookstore outside the US - it does not include 'free' web access in the UK due to data roaming charges incurred by the phone networks here.
BTW, it helps if you put your location in your user profile - then we'd know if you lived in the UK, or were just planning a visit here