FinFET
Beginner
A transistor whose channel stands up like a thin fin, with the gate draped over it on three sides, so it grips the channel better than a flat one.
Novice
A transistor built on a thin vertical fin of silicon. The gate covers the two sides and the top of the fin, which gives it much better control than a flat (planar) transistor. Its width comes in whole fins, so designers use one, two or three fins per transistor.
Expert
A multigate MOSFET (double- or tri-gate) on a fin a few nanometers thick, invented at UC Berkeley in 1998 and in volume production from 2011. Channel width is quantized to per fin; the sub-fin under the gated region needs a punch-through stopper. ASAP7 models 32 nm × 6.5 nm fins on a 27 nm pitch.
Explained in Shrinking (Transistors).
See also: Gate-all-around (GAA) nanosheet, Short-channel effects.