It's exactly what it sounds like, it's your players opinion of you. Most are neutral or happy, but if a player is unhappy, most likely it's due to a lack of playing time. If you want to make that player happy give him more playing time.
Sometimes you'll see a player listed as livid. That's worse than unhappy and probably means you cut or traded the player, although those can also simply be unhappy.
Those opinions of you stick with that player even once off your roster. There have been players I wanted to resign off the free agent list but a pop up says "This player is unwilling to sign with you". If you have any former players on another roster, when you click on their team the opinion of you button reflects their opinion of you, even though they are no longer your player.
