A simple sentence consists of a single independent clause. It expresses a complete thought and can stand alone as a sentence.
Example: "The sun is shining."
A compound sentence consists of two or more independent clauses joined by a coordinating conjunction (and, but, or, nor, for, so, yet) and a comma.
Example: "The sun is shining, and the birds are singing."
A complex sentence consists of an independent clause and one or more dependent clauses. The dependent clause cannot stand alone as a sentence.
Example: "Although the sun is shining, the birds are singing."