A complex sentence consists of one independent clause (a.k.a. a simple sentence) and at least one dependent clause. The independent clause can stand alone, but the dependent clause cannot. Tsk tsk. So needy.
Complex sentences are… uh… complex.
Right now you're probably thinking, "Shmoop, I've got independent clauses on lock. I could pick out subjects and predicates all day long. But what about dependent clauses? How do I spot them?"
Great and perfectly timed question, Shmooper.
Here's the answer: keep an eye out for AWUBIS. While it may sound like a vengeful sorcerer from Outer Wubveria determined to control the weather (or something?), it's actually a useful memory device that represents several of the most common subordinating conjunctions:
If you see AWUBIS, there's a good chance you're staring down a dependent clause.