EE is the new name for “Everything Everywhere” which came about from the merger of Orange and T-Mobile networks in the UK. EE got in the news again because it managed to wrangle permission to launch its own 4G network ahead of everyone else (by refarming space it already had). The 4G network is only available in some cities; London, Edinburgh and 9 others.
Not many phones support 4G yet but that number will very quickly rise, especially after Christmas and lots of smartphones are given as presents. Devices like the iPhone 5 and Samsung Galaxy S3 are compatible.