There are two types of clauses, independent and dependent.
Dependent clauses are sentences that require other sentences to make sense. One example of a dependent clause is:
After Billy came home.
"After" is the subordinating conjunction that makes the clause dependent, does this clause make sense? To make the sentence make sense, we can do two things, add an independent clause to the sentence, or remove the conjunction. This is the sentence after removing the subordinating conjunction:
Billy came home.
This is the same sentence after adding an independent clause:
After Billy came home, his mother made him write about clauses.
This is now an independent sentence because it can stand on its own without adding another clause to it.