Fee-shifting is a method of payment for legal services under which the victorious plaintiff recovers reasonable attorney's fees from the defeated defendant. The model in Europe, American jurisdictions have only adopted fee-shifting in civil rights cases. In these cases, the civil rights plaintiff takes fees from the defendant, as a way of encouraging lawyers to take on civil rights cases from otherwise indigent defendants - the theory is that, (1) civil rights are important enough that the infringer should pay for the infringed party's non-pecuniary loss, and (2) the state should encourage civil rights litigation, and recovery of lost rights, by ensuring recovery enough to entice an attorney.
For example, under 42 USC 1988, a plaintiff may recover fees for a lawsuit which was filed pursuant to 42 USC 1983, the main statutory vehicle for a civil rights lawsuit alleging violation under color of state law. Under this fee-shifter, organizations like the ACLU routinely recover ordinary attorney's fees. Nothing is exceptional about this; it's just statutory law.