A reusable, programmable chip. The circuitry of an FPGA can be programmed to mimic almost any type of digital chip -- a microprocessor, for example. The trade-off is that the FPGA is usually larger and more power-hungry than a specialized Application-Specific Integrated Circuit (ASIC).
FPGAs are useful to systems designers that make their own chips. The engineers will try their ideas in FPGA form first, to accommodate any changes or debugging, later transferring the project to an ASIC.
Sometimes, a vendor will release a system or linecard that's still based on FPGAs, promising that a slimmer, future version will be based on ASICs.
FPGAs used to be compared to cassette tapes that start blank and can have music recorded and re-recorded on them. These days, it's more appropriate (but less satisfying) to compare them to empty iPods.