What is the real meaning and connotation of 'Jihad?'

From my days in a Christian seminary, I was taken to understand that there is a "lesser jihad" (the term most Americans assume is meant) and a "greater jihad" (which is the struggle against one's own sin.) While the term has a clear connotation when used by non-Muslims in the United States, what is the real connotation of the term when used in Islamic circles? Is the first reaction really the "greater" or "lesser" jihad, and what is the practical understanding for "the man in the street?"