Broadcast by ATC to warn air traffic to remain clear of areas such as open air affairs, forest fires, space launches, crime scenes, etc. See material on TCA, ARSA and clearances, surface operation. Each of these areas is sources for deviations from the FARs and reasons for FAA enforcement actions.
Advisory Circular 91-63B dated 2/28/97 explains how a TFR comes into being. Nearly any governmental agency can request and obtain a TFR from the air traffic manager having jurisdiction over the airspace concerned. The primary objective is safety and NOTAMs are kept to a minimum in line with this objective. Airspace limits are usually 2000 and a 3-nautical mile boundary about the area. Special restrictions apply to aircraft authorized to fly inside the TRF area. In the Bay Area and California TFRs are most likely to exist around fires and floods.
Friend of mine was FAA Violated on a non-stop flight from Arizona to Napa when he over-flew Lemore Naval Air Station at 8500. There was NOTAM out regarding an air show. It had to stop while he was in vicinity. It happens.