Xcode: Copy Headers: Public vs. Private vs. Project?

Randy's answer is good and gives you all the relevant background. I wanted to add some info to help you based on how you expect your library will be used.

PROJECT: If you are distributing your project, and expect users to include your project as a sub-project in their own, you should ensure your headers are marked as 'project'. Not doing so will lead to issues like this: Xcode 4 Archive Version Unspecified

Note that this applies to every sub-project...including sub-projects of sub-projects, recursively.

PUBLIC: If you expect users of your library to only link against your object (and NOT have your original project), make sure your headers are marked as 'public' (only for headers they'll need to refer to).

Public: The interface is finalized and meant to be used by your product’s clients. A public header is included in the product as readable source code without restriction.

Private: The interface isn’t intended for your clients or it’s in early stages of development. A private header is included in the product, but it’s marked “private”. Thus the symbols are visible to all clients, but clients should understand that they're not supposed to use them.

Project: The interface is for use only by implementation files in the current project. A project header is not included in the target, except in object code. The symbols are not visible to clients at all, only to you.

Source: Xcode Developer Library > Tools & Languages > IDEs > Project Editor Help > Setting the Visibility of a Header File