Influence of Delegates at National Convention

How much influence do district-level delegates have at the Democratic National Convention?  I received the most votes in my Congressional District as a Dean Delegate.  I and most of the other Dean Delegate candidates talked about how even if Dean is not the nominee, we will work to take back the Party and urge the Party to adopt Dean's policies and values at the national convention.  

Is there any substance to this?  What influence does a district-level delegate really have?  I know the Party's platform is decided upon at the convention.  Does the platform matter beyond making a statement?  And, who really decides what's in the platform?