It's an outdated interface connection standard commonly used by camcorders in the 1990's (mostly MiniDV camcorders I think); its technical name (or name of its specification rather) is IEEE1394, 'FireWire' is just the marketing term Apple used for it. I think Sony called it 'i.Link'.

FireWire400 is really called IEEE1934a and has a theoretical transfer rate of 400 Mb/s, it can deliver 7 watts of power and carry ethernet packets.

The standard pretty much died off as soon as USB 3.0 came out AFAIK, since they couldn't get higher transfer speeds than a theoretical 800 Mb/s (whereas USB3 supports up to 5 Gb/s).

My profile picture shows a FireWire400 port on the front panel of a PowerMac G5.