What term describes an atom's tendency to hold on on to electrons?

The term that describes an atom's tendency or ability to hold on to electrons and pull electron density from other atoms closer to itself is referred to as electronegativity. A very electronegative atom, will not only have a strong attraction to its electrons including the valence ones, but also to the valence electrons of other atoms, usually these are nonmetals.

Explanation:

Electronegativity is the chemical property of an element. This is defined as the tendency of an atom to attract the shared pair of electrons towards itself when a bond is formed.

This property of an atom increases as we move from left to right in a period because the number of charge on the nucleus increases.this property decreases as we move from top to bottom in a group because electrons get added up in the new shells which make it further far away from the nucleus.