It's possible because it isn't impossible. There is no rule in physics or math that says it is impossible, which means it's possible.

And what it is, is basically saying that some subatomic particles can exist in different states at once.

For example, electrons have a property known as spin. Since they have spin they have direction (kind of like how the Earth spins and because of that, has a north and south pole). Since electrons have a direction, an electron can be "up" or "down."

Superposition says its possible for an electron to be put into a state where it is both up and down at the same time, and will only definitely be one (and not the other) when it interacts with another particle.