Example 1
Until ferrets are granted driver's licenses, I'm going to have to keep driving Squiggles to the veterinarian's office.
In this example, the subordinating conjunction until is used to link the two ideas expressed in the sentence. We've got the dependent clause Until ferrets are granted driver's licenses, and the independent clause that follows it. Did you notice that the dependent clause and independent clause are linked with a comma? Excellent.
Example 2
My little sister annoys me because she wants to do everything that I do.
Listen, she might irritate you now because she does things like borrow your favorite sweater without asking, but one day you'll be grateful for her.
And you'll also be grateful that you know that because is a subordinating conjunction. In this example, the independent clause My little sister annoys me is joined to the dependent clause because she wants to do everything that I do.
Example 3
Tacos seemed to rain down from the heavens after the tortilla truck crashed into the chorizo factory.
We've had dreams of this situation. In this tasty example, after is a subordinating conjunction that links the independent clause tacos seemed to rain down from the heavens with the dependent clause after the tortilla truck crashed into the chorizo factory.
The fact that tacos were falling out of the sky is the main event here; that's why it's expressed in the independent clause. The fact that the taco storm started when a truck crashed into a factory, while awesome, is rendered less important because it begins with the subordinating conjunction.