When my girls do it they sing out a whole series of clucks that sounds like they are saying "Look, look, look, look, look what I did"! Then they repeat the exact same thing over and over a few more times to make sure everyone heard them.
Oh that's funny! I didn't know that this was so common it had a name! DH says it sounds like they are saying, "More chickens, mo, mo, more chickens!" What's really funny is that when one starts the 'egg song', all the others join in (my rooster even crows about it!) and boy do they rock the neighborhood!