Petals free: the petals can be extracted one by one from the corolla:

Petals fused: in this case the petals are fused together at least at the base of the corolla: it is impossible to extract a single petal without breaking the corolla:

Beginners often confuse the strap-shaped (ray-)flowers of the Asteraceae for petals. For example, the white flowers of daisies are not 'free petals' but individual flowers with a strap-shaped corolla in which the petals are fused together: