A fire cut joist is a regular floor joist, except for the end where the end of the joist rests on a supporting wall. A regular joist has a square cut end, whereas a fire cut has an angled cut on the end. The angled cut is made towards the top middle of the joist, from vertical. This is done so that if a fire in a building causes the floor to collapse, the floor will fall out of the wall easily. If the joist has a regular square cut end, as the floor collapsed, the end of the joist can push up on the wall above it, causing that wall to tip over.
See picture (courtesy compactdynamics.com)