The icons you're referring to indicate the "visibility" of the board (or organization)
(green dot) means the board (or organization) is "Public". It is visible to anyone (even people without Trello accounts)
("two people") means the board is visible only to members of the organization that the board belongs to.
(lock) means that the board (or organization) is private. A private board is only visible to members of the board, and a private organization is only visible to members of the organization.
(In some contexts, if you hover your mouse over one of the icons, a tooltip will pop up explaining what the icon means.)