What do you do with a dropper in Minecraft?

Just drop stuff but you can out things into chests if the chest is in front, pretty useless.

The dropper is used to drop items or push them into containers. In redstone, they're used for many many things. They're great for item transportation such as item elevators, you can make it give player items, make auto smelting systems and item sorting systems.

The Dropper is an item dispenser that only "drops" items instead of "firing" the item that the Dispenser performs.

The Dropper can be utilized in various redstone mechanics, like a using a bucket of lava to make a mob cooker (with a push-button to briefly "dip" them in lava to cook them). It can also help to transport items (especially upward). The one charcoal generator that I built utilizes 3 droppers to move the charcoal out of the furnace & transport it into the fuel chest for later extraction (& to automatically fuel the the generator).

There's likely some other uses for it, but you'll have to look into it at your leisure.