A simple sentence has a subject and a verb in one independent clause.
The house on the corner is on fire.
A compound sentence has two or more independent clauses.
Kara likes to cook, but she hates cleaaing up afterwards..
A complex sentence consists of one independent clause and one or more dependent clauses.
Jenny got a job in New York after she grauated from college.
A compound-complex sentence consists of two or more independent clauses and one or more dependent clauses.
Although Alice wanted to be a musician, she was tone deaf so she became a lawyer instead.
For more information about sentence types takes a look at
An explanation of the types of sentences in English: simple, compound, complex and compound-complex– www.understandinggrammar.com