As you go across the period from left to right (excluding noble gases), electronegativity increases. This is because the nuclear charge increases (Atomic Number/number of protons) and atomic radius decreases and therefore there is a larger nuclear attraction which bonds the electrons more strongly. Electron shielding remains similar so is outweighed by the other factors.
As you go down a group, the shells get larger which means there is greater electron shielding. The atomic radius increases so the nuclear attraction decreases. The nuclear charge is outweighed in this situation.