The idea that gender is “constructed” means that:

We distinguish between "sex" and "gender".

Your sex is what you're born as, the physical body, you're either a man or a woman. 

Your gender is something that you construct. That means, you may feel like either a man or a woman. 

In some cases your physical sex and your constructed gender don't match, and you have people who feel as if they had been born in the wrong body.