Choosing to make your information public is exactly what it sounds like: anyone, including people off of Facebook, will be able to see it.
Choosing to make your information public also means that this information:
can be associated with you (i.e., your name, profile pictures, cover photos, timeline, User ID, username, etc.) even off Facebook;
can show up when someone does a search on Facebook or on a public search engine;
will be accessible to the Facebook-integrated games, applications, and websites you and your friends use; and
will be accessible to anyone who uses our APIs such as our Graph API.
Sometimes you will not be able to select an audience when you post something (like when you write on a Page's wall or comment on a news article that uses our comments plugin). This is because some types of stories are always public stories. As a general rule, you should assume that if you do not see a sharing icon, the information will be publicly available.
When others share information about you, they can also choose to make it public.