What does the "EU Internet" switch do on my iPhone 5s?
Solution 1:
I believe it allows data roaming, but only within European Union countries. See http://www.cultofmac.com/288360/europeans-new-roaming-options/:
Inside cellular settings, Apple has added a dedicated “EU Internet” switch alongside the existing data roaming toggle. It gives users the ability to active Internet connectivity when they visit countries inside the European Union, while in other parts of the world in will remain inactive.
Presumably, this change follows new European legislation that says carriers can no longer charge customers for data roaming when they visit other EU countries. The rules don’t officially come into effect until 2015, but a number of carriers have already begun abolishing roaming fees.
Solution 2:
On a recent trip to France I found that enabling 'EU Internet' and data roaming did not work (no internet connection), but turning 'EU Internet' option off, allowed the regular Data roaming to work.
Today, I received a txt from Vodafone confirming this and, telling all IOS8 users to turn this feature off (even if they are in Europe)... so it may well be for a future feature, but it's not working (at least for Vodafone customers) just yet - perhaps Vodafone are waiting for the legislation to kick in, and till then we just have to put up with regular Data Roaming charges!
Solution 3:
The simple answer to this is that the EU Internet option is to allow the use of Local Breakout (LBO) providers, who can offer data at a different rate to your "parent network" most home networks will not provide any support if you are using a LBO as the provision is provided through the "EU internet" APN (Access Point Name).
In short if you don't want to use your own network's roaming plan you need this on. If you do you need it off.