Titration reactions involve the implementation of carefully monitored concentrations of acids or bases. In this case, the NaOH being put into the buret has been “standardized,” or very carefully created to have a precise concentration to use in calculation.
Washing the buret our with water will help to clear out other contaminants, but the adherence of water to the sides of the buret will affect the concentration of the solution put inside of it. By adding water to the solution, it is being diluted to a small degree, which will tip the equations in the wrong direction to say that the unknown being tested is MORE concentrated than it actually is, because more liquid is required to titrate it to completion.