So Stay and Scream is essentially early entry for HHN. It is available to anyone who has both a valid park ticket for USF (as they need to be in the park itself before it closes at 5pm.), and a valid HHN ticket for that night.
How it works is very simple, you first enter USF, and around 4pm the various Stay and Scream holding pens will open, you present your valid HHN ticket to enter them. You have to be in one of them before the park closes at 5pm.
Inside the Stay and Scream holding pens, you'll have access to whatever food is available inside them, and some of them such as the New York area will have their specialty food booths open. Also, the holding pens offer one or two houses for you to queue for. New York offers two sound stage houses, San Fran/Richters offers the house in Fast and Furious, Springfield usually offers both Parade Warehouses (however that might change due to the portals/queues moving around due to KZ construction.).
Around 5:45pm give or take, it depends how fast they're able to get everything ready, they'll start letting folks into the queue for the houses and into them. Depending on the lines and such, you can get in one or two houses before everything opens up at 6pm. (Keep in mind, they'll hold you in your respective area until 6pm. So you can only do the houses that are open in that area.)
Stay and Scream can be a great way to take care of one of the really big IP's early on (even moreso if the event ends up having multiple big IP's. If there's just one, you can probably save that for last. But if there's several, hitting one in Stay and Scream could be vital.), and it gives you a great head-start on hitting up the houses in the back of the park before they start getting busy.