What is the purpose of DNA?
Imagine you want to produce a widget. You have thousands of worker, but only one blueprint. Each worker needs the blueprint to build a widget (they're really forgetful and can't build from memory). So only one worker at a time can build your widgets.

What you would do is to create copies of your blueprint and distribute them to your workers. That way multiple workers can produce the widget at the same time.

DNA is the blueprint, and RNA is the copy. Your workers are the ribosomes that translate the RNA into proteins. 

This is of course grossly simplified, and there are other reasons for the specific arrangement, but this is certainly one of the reasons why the intermediate RNA is used.