I don't understand Refinancing

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Hi Guys, 

Sometimes its the simplest concepts that I overthink, but I am having a bit of trouble comprehending a refinance. Lets assume I take out a mortgage for X amount amortized over 30 years at 6%. When I refinance, does the balance stay the same (effectively making me start the payment process all over again)? Or do I only apply for the amount that I owe since I will have built some equity in the property. Also, I don't understand how a new down payment would be needed when refinancing. Am I meant to to bring 20-30% of the appraised value?

Simple concept that I am almost sure I am over-analyzing, but I would appreciate your guys' help.

Thanks.