A cleft sentence is a complex sentence that expresses a simple sentence by way of a main clause and a subordinate clause. Sure, that's a nice, highfalutin definition, but what does it all mean? A simple example can perhaps clear up the meaning. Consider this simple sentence:
Lex Luthor attacked Superman.
This is a normal answer to the question, Who attacked Superman? But perhaps someone didn't hear you clearly and asked, "Did you say that Lex Luthor attacked a Sumerian?" You might want to answer with a cleft sentence to place the emphasis on the information in question — that is, Lex's intended victim. That cleft sentence would look like this:
No. It was Superman whom Lex Luthor attacked.
This cleft sentence expresses the same information in the original simple sentence — Lex Luthor attacked Superman. — by way of a main clause, It was Superman . . . , and a subordinate clause,
. . . whom Lex Luthor attacked, but places the most important piece of information closer to the beginning of the sentence.
Related to the cleft sentence is the pseudo-cleft sentence, in which the subordinate clause is a relative clause that begins with an interrogative word — who, what, where, and so on — at the beginning. Here's an example:
What Lex Luthor threw at Superman was kryptonite.
If you switch the order of the main clause and relative clause in a pseudo-cleft sentence, you get an inverted pseudo-cleft sentence:
Kryptonite is what Lex Luthor threw at Superman.
Both of the above examples are complex sentences that express the same information that's in the simple sentence, Lex Luthor threw kryptonite at Superman.
Cleft, pseudo-cleft, and inverted pseudo-cleft sentences serve to shift the focus of the sentence to its most important element. This shift is more evident during speech because one naturally emphasizes the word or words that are the most important bits of information.