Permutation representation

I clicked on this link as I was trying to figure out what on earth a "composition" of two permutations (the * operation) could possibly mean. I am just using this space to comment (you can delete this). oops.. I just realized what it could mean.. two permutations, one after the other on a string of objects. Of course this specific temporal imagery may be irrelevant (maybe a spatial metaphor could also be used?).. again these are just free associations.. feel free to zap these.