the Head of Product for any company is responsible for three major things:

1) Setting the overall product strategy and vision.
2) Coming up with simple and creative solutions to the most complex problems.
3) Getting things done and shipping product by saying no to 99% of feature ideas.

Each team is setup differently, so your head of product can have a great design, technology, or product management background, but at the end of the day, his/her main focus is to make sure the ship is steering in the right direction. (Keep in mind that your Head of Product is NOT your Product Manager. Product management is one small snippet of the overall responsibility.)