What does the mirror do?

Mirrors will show an unlocked chest in their reflection. The chest can be opened, which will shatter the mirror and increase the player's curse. The mirror will also shatter if the player shoots it, which will increase the player's curse and make the chest inaccessible.

http://enterthegungeon.gamepedia.com/Mirror

you can open the chest or break it, both options will curse you.

If you want to open the chest, you have to step away from it, and if you press "E" (or "A" on controller) when your reflection is facing the chest, an object or weapon will apear and the mirror will break.

I'm not sure what curse is for, but I think one of it's effects is that you have a higer chance to find stronger enemies.