What do you mean, you travel a thousand miles and I fall with your beauty?

It implies an emotional state of infatuation and attraction. "Waving countless ties" can be understood as someone waving many tiny threads or fibers, which vividly describes a beautiful gesture or action. "I fell in love with your beauty" expresses followers' indulgence and infatuation with this person's beauty. This sentence may imply an emotional state of infatuation and attraction.