The shielding effect is a consequence of electrons surrounding the positively charged nucleus when you add a new electron to the outside of an atom. Consider first a lone electron placed a certain distance away from a positively charged nucleus with no extra electrons in between. It would feel a certain attractive force towards the positively charged nucleus. Next place an additional electron directly in between the nucleus and the electron in question. The electron on the outside would still feel an attractive force towards the nucleus, but the effect would be lessened by the repulsion of the electron that now appears in between our original two particles.
The better the inner electrons shield the nucleus, the farther away an outer electron will be from the nucleus when we add it. Now different orbitals "shield" the positively charged nucleus more or less effectively. As you move up the periodic table you are adding another positively charged proton at each step, making the nucleus attract electrons more strongly. In the absence of shielding you would predict that each additional charge will make the radius of the atom smaller and smaller as the electrons are pulled in closer by the larger positive charge. However, the electrons that were added to the atom in previous steps will repel your added electron so that the effect of adding an additional positive charge will be less than you would expect. Since the d-orbitals shield the nucleus poorly (which they do because their electron geometry is more "open" then the s and p orbitals), the outer electron is able to "feel" the additional positive charge being added to the nucleus more than it would if the shielding was better. So the outer electron is pulled in closer towards the nucleus in gallium then one might expect. As a result its radius is smaller than aluminum.