Kolpak ruling (as simple as it can be put)
The ruling is named after a Slovakian handball player, who said that he should be able to play in Germany as a non-overseas player, because Slovakia had an associate trading agreement with the European Union (EU).
The case went to the European courts, and they ruled in his favour.
This meant that anyone from a country with an associate trading agreement with an EU country can have the same employment rights as anyone from the EU.
For cricket, this means that anybody with an EU passport can not be classed as an overseas player. The same now applies to players from these countries with associate trading agreements.
For English cricket, the Kolpak ruling applies to players from South Africa, Zimbabwe and Jamacia, as well as several non-test countries. The players will not be eligible to England, but have to sign a document saying that they hae no intention of playing for their country again.
If a player has an EU passport, they do not come under the Kolpak ruling, eg. Andy Flower and Nic Pothas. They also have to sign a document stating the same as above.
Genuine EU players (ie. those who are eligible to play for a European country (Amjad Khan, Ryan ten Deshoate) ) do not have to sign any such agreement.
Hope that clears things up for you.
note: Despite what the game says, Australians can not be Kolpak players.