Attrition is a gradual process of wearing down, weakening, or destroying something.
When a company wants to reduce its payroll without firing anyone, it will sometimes do so through attrition; that is, by waiting for people to retire or quit without hiring anyone new to replace them. In a more general sense, the word means break down, wear out, or reduce in numbers. A triple overtime basketball game, with many players fouling out, is a war of attrition. When you see the word attrition, think "Gradually chipping away."