Mick is talking about American "Irish-style" sessions, I guess (from his use of the neologistic and -sorry- rather bogus transliteration "seisun") but it's much the same in the UK: two or three times through for a dance tune, then on to the next one. They are dance tunes and still played in that format (though often ridiculously fast by players who wish to show off or who have no experience of playing for dancing).

The practice of playing dance tunes in pubs without dancers is quite recent; in England it would have been seen as very odd until the 1960s. It seems to have begun in the Irish "revival" sessions that developed from the post-war model, and spread from there. American-style Old-Time and Bluegrass sessions seem to be a different breed; in the latter case it appears that the tune is repeated until all participants have had the opportunity to play a solo. In the former case it can sometimes be difficult to see why they bother; though at times repeating a tune until none of the musicians are playing it any more can certainly be educational.