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. 

  

 Xilinx are the biggest FPGA company at the moment, [http://www.xilinx.com].