Your head position and where you look during a squat have very subtle benefits. You'll be able to keep your balance throughout the exercise better, concentrate on your lift and be more consistent with performing the exercise the same way every time.
Alan Thrall, owner of Untamed Strength in Sacramento, California, explains that it's better to look at something in front of you when you squat to help with focus and stability. Because if you're not stable, your squat will suffer.
Personally, I avoid squatting while facing a mirror because I'd be tempted to just watch myself than actually focus on my squat (two different things). If I have to, I'll fixate on my shirt logo or something.
Thrall also advises that you keep your head aligned with the rest of your torso. In other words, avoid intentionally looking up or down, as that would mean you have to flex your neck and spine to do, which could give you issues like exertion headaches when you squat with heavier weight.
I'll admit that this concern over looking up or down is a bit of an anal retentive detail, but whatever helps you lift a few more kilos, I say! Ultimately, what matters more is that you're able to stay balanced with good form throughout the squat and be consistent with every lift.
Where Should I Look While Squatting? [Alan Thrall]