The way that I explained this to my family at a recent family reunion was that all 1st cousins have the same grandparents in common. Likewise, 2nd cousins have the same great grandparents and third cousins have the same great great grandparents. Once that was digested, I then explained that the once or twice removed was the number of generations away from your 1st, 2nd, or 3rd cousins. It sounds more complicated as I type this out but they all got the point.