Invitationals are optional fun meets for the swimmers to attend.  Going to invitationals offers more competitive opportunities for your swimmer to swim.  If your swimmers wants to pick what events he/she will swim than invitationals are the chance to do that. 

League meets the coaches will decide what the swimmers will swim.  Sometimes a swimmer may swim the same events at each league meet.  Invitationals gives the swimmer a chance to try different events.