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a reduction or decrease in numbers, size, or strength:
Our club has had a high rate of attrition because so many members have moved away.
a wearing down or weakening of resistance, especially as a result of continuous pressure or harassment:
The enemy surrounded the town and conducted a war of attrition.
a gradual reduction in work force without firing of personnel, as when workers resign or retire and are not replaced.
the act of rubbing against something; friction.
a wearing down or away by friction; abrasion.
Theology. imperfect contrition.
See under (def 2).
Contemporary Examples

Their numbers grew, attrition was minimal, and morale was plenty high.
Israel’s Religious Zionist Vs. Ultra-Orthodox Rift Rabbi Daniel Landes February 6, 2013

It is not a decisive war, with a single, signature victory, but a war of attrition.
Pentagon Doesn’t Know How Many People It’s Killed in the ISIS War Nancy A. Youssef January 6, 2015

Getting in now to win local hearts and minds is the only way to prevent this war of attrition from worsening further.
The Government of Pakistan Needs to Step Up Parag Khanna April 23, 2009

But there is no consensus about what the attrition of ISIS looks like.
Pentagon Doesn’t Know How Many People It’s Killed in the ISIS War Nancy A. Youssef January 6, 2015

The past two months have been a war of attrition between the Hong Kong government and pro-democracy protestors.
The Monuments Men of Occupy Hong Kong Brendon Hong December 3, 2014

Historical Examples

Water and attrition soon round these minerals on their sharp edges, and thus show that they have come from some little distance.
The A B C of Mining Charles A. Bramble

Nothing has done us more harm than all this talk about “attrition.”
War Letters of a Public-School Boy Paul Jones.

Or her constitution—physical and spiritual—had succumbed to the attrition of duty against womanly instinct.
Jessamine Marion Harland

The difficulty was to overcome its susceptibility to attrition.
Mizora: A Prophecy Mary E. Bradley

It grew better and brighter with the attrition of repeated delivery, and was fresh and new to every new audience.
Ars Recte Vivende George William Curtis

noun
the act of wearing away or the state of being worn away, as by friction
constant wearing down to weaken or destroy (often in the phrase war of attrition)
Also called natural wastage. a decrease in the size of the workforce of an organization achieved by not replacing employees who retire or resign
(geography) the grinding down of rock particles by friction during transportation by water, wind, or ice Compare abrasion (sense 3), corrasion
(theol) sorrow for sin arising from fear of damnation, esp as contrasted with contrition, which arises purely from love of God
n.

1540s, “abrasion, a scraping,” from Latin attritionem (nominative attritio), literally “a rubbing against,” noun of action from past participle stem of atterere “to wear, rub away,” figuratively “to destroy, waste,” from ad- “to” (see ad-) + terere “to rub” (see throw (v.)). The earliest sense in English is from Scholastic theology (late 14c.), “sorrow for sin merely out of fear of punishment,” a minor irritation, and thus less than contrition. The sense of “wearing down of military strength” is a World War I coinage (1914). Figurative use by 1930.

attrition at·tri·tion (ə-trĭsh’ən)
n.
A wearing away by friction or rubbing, such as the loss of tooth structure caused by abrasive foods or grinding of the teeth.