In Node.js, the EventEmitter class allows adding listeners that respond to events. Using the 'once' method adds a listener that runs only the first time the event is emitted. When the event is emitted, the listener runs and then removes itself automatically. If the event is emitted again, the listener does not run because it no longer exists. This behavior is useful for handling events that should only trigger a single time. The execution table shows the listener count starting at zero, increasing to one when added, running on the first emit, then dropping back to zero after removal. The second emit finds no listener and produces no output.