As I already stated, the biggest advantage is "access." Having a big name politician on your board means you can have them chat with their friends in congress about why they should vote yes/no on a certain bill. It helps the company convey their opinions to the people who matter. There are other advantages, like increasing the organization's prestige, and having access to someone with a great deal of knowledge about the political process (who might be persuaded, who is a lost cause, etc.)