What is meant by the statement that the electric field of a point charge has spherical symmetry whereas that of an electric dipole is cylindrically symmetrical?

Consider a charge q at the centre of a sphere of radius r. The electric field at all points on the surface of the sphere is given by

So, the electric field due to a point charge is spherically symmetric.

In the case of an electric dipole, the electric field at a distance r, from the mid-point of the dipole, on the equatorial line is given by

Now, imagine a cylinder of radius r drawn with electric dipole as axis. The electric field, due to dipole, at all points on the surface of the cylinder will be the same. So, the electric field due to dipole has cylindrical symmetry.