When we look at really really small stuff, we can't actually see it with light, because it's so small light can't bounce off of it like it does large objects like cats. The only way we can "see" these tiny tiny things (ie electons) is to hit them with other small things. However by hitting them, we've imparted a force, which changing the way they are behaving. So we can't actually see anything on the quantum scale and know how it usually behaves, only by how it behaves when it's getting hit by stuff.
So, all we can do is say "half the time, when I hit an electron, it was moving left, and half the time it was moving right. For this reason there's a 50% chance that any particular electron is moving right, and a 50% chance that it's moving left."
However, until we hit the electron to see which way it's moving, we don't know. And, there's been experiments that show that the electron isn't sure either. So, we say that it exists in both states (moving left and right) until we hit it, and force it to choose either left or right. (“Spin” left/right)