Sleeping outside in the backcountry without an overhead shelter (such as a tent or tarp), usually done in the context of backpacking. The decision to cowboy camp is a calculated one - bugs, rain, snow, etc. are all possible backfires to the decision and can damper the experience.
Note that having an adequate shelter is a must, cowboy camping is the decision to forgo setting up a dedicated shelter and betting that conditions will be such that the shelter is not needed (but the dedicated shelter is still present/available should it be needed). Not bringing adequate shelter with you into the backcountry is foolish and can result in injury or death.
Last night we went cowboy camping at Panther Gap and the stars were ridiculous.