I'm a photo student and we had an assignment about exposing our images correctly. We were told to expose one correctly and 1 stop over, 2 stops over, 1 stop under, 2 stops under and then take all the images into photoshop and make the highlights, mid tones, and shadows all even with every photo. Unforturently I couldn't find the proccessed images so I have done a quick process job to show you the basic idea.
These pictures were just for demonstrative purposes, not serious portraits.
1 stop over (then pulled 1 stop down in post):
2 stops over (then pulled 2 stops down in post):
1 stop under (then pushed 1 stop over in post):
2 stops under (then pushed 2 stops over down in post):
As you can see there is quite the difference in these images.
-Underexposing an image and adjusting in post brings out the noise and
-Overexposing an image and adjusting in post reduces the contrast
I hope this helps you understand the importance of exposing an image correctly.
Citruspers is right that underexposing images results in more contrast but that is something that can be better achieved by adjusting the levels and using the contrast slider.