Why does electronegativity increase across and up the periodic table?

Electronegativity increases across a period (left to right) and up a group because of the combined effects of atomic size and effective nuclear charge. Electronegativity is the ability of an atom to attract the shared pair of electrons in a covalent bond. As you move across a period, the number of protons increases while electrons are being added to the same shell, resulting in a higher effective nuclear charge, which is the net positive charge experienced by valence electrons after accounting for shielding. Since the shielding remains relatively constant across a period (same number of inner shells), the increased nuclear charge pulls the valence electrons more tightly, making the atom smaller and better able to attract bonding electrons. This is why fluorine, at the far right of Period 2, is more electronegative than carbon or nitrogen in the same period.

Moving up a group, electronegativity increases primarily due to decreasing atomic size. As you go up a group, there are fewer electron shells between the nucleus and the bonding electrons. For example, fluorine (Period 2) has only two electron shells while iodine (Period 5) has five. When atoms form covalent bonds, the shared electrons in smaller atoms are much closer to the nucleus and experience a stronger electrostatic attraction, despite the smaller number of protons. The effect of decreasing distance outweighs the effect of decreasing nuclear charge as you move up a group. These two trends combine to make fluorine, located in the upper right of the periodic table, the most electronegative element with a value of 4.0, while francium in the lower left would be the least electronegative.

The only exception to the trend is the noble gases, which typically don't form bonds and therefore don't have standard electronegativity values.