The larger the difference in electronegativity between two atoms, the more ionic the bond. This is because more electronegative elements (fluorine, for example) are more easily able to take and retain electrons in ionic reactions.
Ionic bonds are formed when two atoms with a large electronegativity difference react. The more electronegative element takes an electron from the less electronegative element. In hydrogen flouride, for instance, the fluorine takes an electron from the hydrogen. However, the less electronegative hydrogen still exerts a pull on that electron. As the difference in electronegativity rises, the strength of that pull relative to the strength of the more electronegative atom's pull decreases, making the bond more ionic in character.