A constructor constructs (i.e. initialises) the object, and the point of a ctor is to do that automatically rather than you having to do that manually.

So the line
Code:
Student a;
will automatically call a.Student() for you. Here's how to write a constructor that initialises Student's attributes to zero:

Code:
class Student
{
  private:
              int idnum;
              double grades[5];
              int totnumgrades;
  public:    
             Student()
             {
               idnum=0;
               totnumgrades=0;
               for (int i=0; i<5; grades[i++]=0) ;
             }
//...
};