LUT (lookup table)
Beginner
A tiny table of answers inside an FPGA. The inputs pick a row, and the table gives back the answer stored there.
Novice
The basic logic element of most FPGAs: a K-input truth table stored in configuration bits and read through a multiplexer whose select lines are the inputs. It can hold any function of its K inputs.
Expert
A -bit SRAM mask read by a K-level mux tree, so delay is fixed by K, not by the function. Modern parts use K = 4 to 6, often fracturable into two smaller LUTs with shared inputs; some can also act as small RAMs or shift registers.
Explained in Lookup tables and the FPGA fabric (Architectures).
See also: Logic block (CLB, LAB, slice, ALM), Configuration memory, FPGA.