When we replace a current carrying circular loop with an equivalent magnetic dipole, the quantity that is not altered is ‘Magnetic moment’.

We know that, for a circular loop of area A and current I, the magnetic moment is,

So, when we replace it with a a dipole of pole strength m and in-between distance d, the magnetic dipole should be same as the first case, hence

So, the product of pole strength, m and distance d should be fixed, even though they are not fixed individually.