Standing wider puts your legs at a more diagonal angle which has the effect of shortening the horizontal distance between your hips and knees. A wider stance will also allow you to be more upright when squatting.
Explanation: By decreasing the distance between your hips and the bar, you don’t have to lean over (as you do with low bar) as far forwards to get the bar over the middle of your foot (the bar being over the middle of the foot is the idea position). You've probably seen this pic before:
Wider stances changes the moments (remember physics and moments?
http://physicsnet.co.uk/a-level-physics-as-a2/mechanics/moments/) involved in squatting to your advantage. However, it also mitigates the disadvantage of the low bar position. When you squat with a wider stance you kinda get a bit of all the win, a more upright hip dominant squat with small moment arms.
That said, low bar squat will be more powerful/stronger generally, as you will be using more posterior chain when low bar squatting and less quad, and your PC is MUCH stronger than your quad. High bar is less PC dominant and more quad dominant.
Irrespective of low or high bar though standing wider will also reduces your ROM - which helps. IF you think about it, your wider position of the legs is going to reduce the vertical distance between the hips and the knees.
Remember for a proper squat ROM you have to bring the crease of the hip below the knee.
It is also down to physiology, short limb length vs long torso and vice versa. I have quite long legs, and fairly equal torso so for me wider stance gives me a better chance of getting to depth.
IF you're long torso short femur - then you have the best physique for squatting. You'll have such short range of motion even with a medium width stance that you should be able to squat a huge amount.
To work out if you are long or short femur lengthed, measure from your hip to the outside of your knee joint. Divide that number by your height in inches or centimetres.
If you get .26 on the dot, then you're average joe bloggs.
>.26, you're trending towards being long femured
<.26, you're trending towards long torsoed