A simple sentence has only one clause. The cat is sleeping.
A compound sentence has two or more clauses. These clauses are joined together with conjunctions, punctuation, or both. The dog is happy, but the cat is sad.
A complex sentence has one clause with a relative clause. The dog, which is eating the bone, is happy.
A complex-compound sentence (or compound-complex sentence) has many clauses, at least one of which is a relative clause: The dog, which is eating the bone, is happy, but the cat is sad.