Question:
Does the plan benefit the children for who the savings are being made? Or does the plan save the parent some taxes? I am not too clear.

Answer:
Though the plans differ from state to state, they are all exempt from federal income tax, and that can give a real bottom-line boost to your college fund.

A 529 plan is a state-operated investment plan that gives families a federal tax-free way to save money for college. Authorized by Congress in 1996, they are officially known as qualified tuition programs (QTPs), but commonly referred to as "529 plans," "state 529 plans," or "section 529 plans" after the section of the IRS code that provides the plans' special tax breaks.

You should view the link below to see an explaination of the different types of 529 plans.