A complex sentence is a sentence consisting of an independent clause and a subordinating clause. Or, to put it more simply, complex sentences involve more than just a straightforward noun + verb. Complex sentences include extra phrases added to a base sentence, but which cannot stand alone as a sentence. For example:
Published 4:00 am, Thursday, January 9, 1997. 1997-01-09 04:00:00 PDT Yosemite National Park -- Yosemite Valley is slowly drying out after what park rangers are calling the worst flood here in recorded history, leaving behind hundreds of upturned tent-cabins and acres of wrecked camping sites.
Date: October 14, 2008. A rockfall occurred in Yosemite National Park at approximately 7:00 am on October 8, 2008 near Curry Village in eastern Yosemite Valley. Park officials estimated the rockfall volume at approximately 1,800 cubic yards, which released near the halfway point up the granite face above Curry Village. Three visitors received minor injuries during the incident.