Public commitments are stating one's intention to perform a behavior or achieve a certain outcome so that others become aware of it. The commitment need not be truly public (i.e. possible for any person to learn), and can be limited to family, coworkers, a small group of friends, etc.
Public commitments are often layered with rewards (e.g., "I will walk 10 miles for every $100 donated by my Facebook friends") or punishments (e.g., "I will do [something embarassing] if I fail to follow-through"). Public commitments are a form of commitment device, where loss of social status or other social consequences may be implied.
Some studies have found mixed results with public commitments, so this tool should be handled carefully. It is believed that in some contexts, some of of the benefit someone receives from performing a behavior or reaching a goal is actually imparted by the social status they receive in stating their intention to do so. Thus, the actual performance become less important (especially when compared with the cost, which is typically borne over many weeks or even years).