Any country that wishes to participate in world football will have a governing body that is known as their Football Association. The Football Association sets rules for the domestic leagues that they must comply with. A Football Association has other effects and it's own tournament. A nation without an FA cannot be part of a football Federation.
A club must be associated with a county's FA to participate in it's leagues and tournaments.
Main Article: FA Cup
An FA Cup is a tournament that any club associated with that particular Football Association can participate in.
Main Article: Association Grown
If a player has been at a club associated with an FA for long enough he will gain a status that may affect whether he can participate in certain competitions.