Recorded in the Song dynasty memoir 《老学庵笔记》 by 陆游: '乃知朝士妄想，自古已然，可付一笑' - 'thus we see that court officials' delusions have always been so; one can only laugh them off.' From 'one laugh' (一笑) the four-character form crystallized into today's idiom.
usage
The phrase implies dismissing something so trivial or absurd that it's not worth a real reply - closer to English 'laugh it off' than to genuine amusement.
