What does "ushr" mean, and what is its religious basis?

In its literal sense, "ushr" means "one-tenth." As a religious term, it refers to the zakat (alms) given from agricultural produce. The obligation of zakat on agricultural products is established by the Qur'an.

Almighty Allah says, “O you who believe! Spend from the good things which you have earned and from what We have produced for you from the earth.” (al-Baqarah, 2/267); “It is He who produces gardens trellised and untrellised, date palms, crops of different kinds, olives and pomegranates, similar and dissimilar. Eat of their fruit when they bear fruit, and give its due (zakat and charity) on the day of its harvest, but do not be wasteful; indeed, He does not love the wasteful.” (al-An‘am, 6/141).

The rate of zakat for these products was determined by the Prophet Muhammad (peace be upon him) himself. In a hadith, it is stated: “On crops irrigated by rain or river water, one-tenth is due; on those irrigated by other means (with effort and expense), one-twentieth is due.” (Bukhari, Zakat, 55 [1483]).

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu