A double-sided key is a flat key with teeth cut into both edges, one along the top and one along the bottom. It is normally symmetrical, so it goes into the lock either way up.
You can recognise it because, looking at it side on, you see the same saw-tooth pattern on both edges. It turns up in some lock cylinders and locks on house doors, in padlocks and in furniture locks.
It is a convenient key, but most of the models that use it offer only basic security. If you have one on your front door and you are concerned about what it protects, it is worth having the cylinder checked. It is all explained in lock cylinder replacement, where you will see when it pays to move to a better quality one.