In a tournament your chips to not accurately represent actual $-value.
Imagine you are in a normal 9-handed sit and go with a buyin of $100 and 1000 chips each. Payouts are 50%/30%/20%
When you start the tournament 1,000 chips is clearly worth $100 because that's what you paid to get them. BUT! When you win the tournament it is obvious they are worth less because 10,000 chips are now worth "only" $500. The tournament chips are worth 50% of what they were when the tournament started.
ICM tries to better calculate the $-value of tournament chips. It works like this:
The problem with ICM it becomes very complex and time consuming if there are a lot of players and a lot of prizes.
Very easy example where very player has the same amount of chips. When everyone has the same amount of chips you can just divide the prize pool among the players, but I will show how ICM arrives at the same number.
Player1: 3000 chips
Player2: 3000 chips
Player3: 3000 chips
Player1 has a 33% chance of winning. This gives him $450 * 0.33 = $148.5 in equity
Player2 also has a 33% chance of winning. If Player2 wins then Player1 has a 50% chance of getting 2nd place (3000/6000 chips). $270 * 0.33 * 0.5 = $44,55 in equity
We repeat the last step for Player3 which gives Player1 another $44,55 in equity
Player1 has a 100% chance of getting 3rd place if Player2 wins and Player3 gets 2nd place.
This gives us: 0.33 * 0.5 = $29,7 in equity
Lastly we must add the last way Player1 can get 3rd place which is when Player3 wins and Player2 gets 2nd place: 0.33 * 0.5 = $29,7 in equity
If we sum these up we get: 148.5 + 44.55 + 44.55 + 29.7 + 29.7 = $297 in equity total
The real number is 300. We lost $3 because we only used two decimals in our calculations.