Acronym for Field Programmable Gate Array.
An FPGA is a (usually) digital device that allows in-system reconfiguration. In it's simplest form an FPGA is a bunch of functional units or CLBs/slices, which each have a multiplexor and a number of gates etc. These CLB's are connected by a matrix of interconnects with MOSFET to (dis)connect them. Although the exact layout of the chip is fixed, the electrical layout is re-configurable by re-programming the FPGA with a core. http://www.opencores.org has a whole bunch of cores (FPGA design files) written in VHDL or Verilog. You can include these in designs free of charge.