You get Iced when you or your opponent's health drops under 20 points (this is a Knockout) during a fight. This is not to be confused with snuffed, which is when you die or when you kill an opponent (the screen will still say You were iced. Heal yourself at the hospital, however).
This includes attacking, defending, and Boss Fight.
When this happens to you, you will not receive a pop-up warning, but you won't be able to spend your stamina unless your heal yourself. It will not count towards your Fights Lost stats if you win the fight, nor if you lose in a Boss Fight.
However when you ice another player, you'll get a pop-up allowing you to share with your mafia in addition to increasing your Mobsters Iced (Body Count) and Fights Won stats.
You can't get iced if your health is under 20.
There is no limit on how many times you can Ice an opponent or be Iced by an opponent. Just keep in mind that when you heal yourself you're actually allowing others to ice you once again and won't be able to heal again until getting iced or losing a substantial amount of health first.