Does the human body convert water?
Yes, the human body "converts" water. 

Out of the hundreds of chemical reactions going on in the human body, there are reactions which take water as an input and "react it away" into something else. There are also reactions which create water out of other molecules. 

Example 1: Hydrolase reactions. They have the form of 


  A–B + H2O → A–OH + B–H 


You get water as input, and something else as output. 

Example 2: Peroxidases "defuse" the highly reactive hydrogen peroxide, producing water. For example, look at the L-ascorbate peroxidase, which catalyzes 


  L-ascorbate + H2O2 → dehydroascorbate + 2 H2O 


Beside these reaction, there is also a lot of water which doesn't react and is simply excreted after having served its purpose. So, while some water is "converted", some other part "passes through". 

The reactions are balanced in such a way that normally, you excrete the same amount of water as you drink, as explained in Amory's answer. But despite this balance of the amount, you cannot claim that the water just passes the body unchanged. Some molecules of it are used up, and others are created de novo.