The answer to that question seems easy: Because it's night, duh. But on second thought, you'll remember the sky is actually littered with stars, and even though our sun is pretty close, it seems like a few hundred thousand (Hundred million? Hundred trillion?!) other stars should at least put out a better glow.
There is, of course, a very good answer for this, and it involves both the limits of the universe in time -- not space -- and the weakness of our puny human eyes. There's more to it than just that, but it get's complicated, so I'll let MinutePhysics explain. Suffice it to say, you won't see the night sky the same way again. [YouTube]