Everytime you see an Ad in NeoBux, you receive 4 opportunities to earn a prize in the AdPrize lottery. The prices include money (up to $50), points (up to 10,000) or a Golden Membership.
Once you get chances, you have 4 hours to use them before they vanish.
Also, when the Ads get refreshed for you, any AdPrize chance that you had left is lost, as you will be getting new ones from the new Ads. You can see when it resets for you in your View Advertisements section of NeoBux:
As an Advertiser, the permanent change in AdPrize means that your Ads will get 33% more exposure in the AdPrize lottery.