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.
Visiting in Summer. Yosemite Falls--and other waterfalls in Yosemite--reach their peak flow near the end of May, but usually remain high well into June. By August, waterfalls have little water or (in the case of Yosemite Falls) may be dry.