An electric dipole moment is defined as $p = q\times 2d$. How to understand it physically? Why the direction of the electric dipole moment is from negative charge to positive charge?
There are two separate issues here. (1) Why does it make sense to consider a dipole moment as a vector? (2) Given that it's a vector, why does it make sense to say that it points in this particular direction, rather than the opposite direction.
There are many, many arbitrary choices of sign like this in physics. If Ben Franklin had made the opposite choice for the sign of the charge of cat fur rubbed on glass (or whatever it was he used as a standard), then we'd say today that electrons had positive charge. The direction of the magnetic field is also arbitrary and could have been defined as pointing the opposite way (in which case some of the signs in Maxwell's equations would flip).