The insert locks the nut against the screw as a result of friction, caused by the radial compressive force resulting from the deformation of the nylon.
[1] There are no registered trademarks filed in the United States for "Nyloc" or "Nylock" that are currently active in regards to fasteners.
For example, Carroll Smith (Carroll Smith's Nuts, Bolts, Fasteners, and Plumbing Handbook) notes that the nylon insert is not damaged by installation and therefore they can be reused many times,[1] and a Federal Aviation Administration Advisory Circular allows nuts to be reused if the prevailing torque is within specification.
[4] However, a United States Air Force Technical Order requires replacement of self-locking nuts in critical areas.
[5] Various specifications for aerospace-grade self-locking nuts require that the running torque be maintained after a number of cycles of assembly, but without preloading the fastener.