Public poker leagues are visible by everyone, including non-site members (To test this, you can log out of PokerDIY and view your league). Private poker leagues can only be seen by league members.
Most of the time it's ok if your league is public, although you may want to hide it by making it private if you are displaying your address or personal information. Sometimes you don't want any new members and can't be bothered showing it off so you could set it to private.
Bear in mind that a poker league can be Public and Invite Only. This means that anyone can see it but only the league owner can add them as a member. Non-members can not write on the league wall or do anything with the league.