Simple sentences are one sentence such as
Joe waited for the train
Jack liked pie
Or LaCie liked to skate
A compound is putting two sentences together, a compound sentence has two clauses like
He sang a song, and she danced….
Clause 1: he sang a song
Clause 2: she dances
Other examples are
We went to the park, and Lacie jumped in a puddle.
Jackie liked rollercoasters, but she often got sick.