What does the question mean when it says did I or did I not support myself through out the year? If o say I didn’t how would that affect my tax refund?

The question being asked to determine if you can file independently or you're a dependent of someone else. It makes huge impact on your tax refund. Being dependent means you only allowed to refund federal taxes paid on excess your deductions, all tax credits will be disallowed.  

it is an important question because it can affect your tax which in turn affects your refund.