OP, chips don’t correspond directly to money in tournaments. ICM is an algorithm to go from everyone’s stack in chips to everyone’s stack in dollars. It’s particularly useful for making shove/fold decisions in one-table tournaments and final tables.
My understanding is that ICM concepts become important near the bubble and near any significant pay jump. Of course the final table generally has pay jumps for every player. The Chip Model will help us understand if making a marginal play is worth it. Generally it isn't, if we are close to making some money, since $0.00 is the outcome of being wrong. Once we cross the money bubble, ICM confirms that not much changes on some of the marginal plays. as the money isn't significant and/or the pay jump is a small percentage of the result of the decision.
Also at the ICMPoker web site is a free ICM calculator for final table calculation info.
As others have said, ICM stands for Independent Chip Model, and its a simple way of estimating, how much chips are worth in a tournament. In a winner takes all tournament this is very simple. Lets say 3 players started with 1.000 chips each, and the winner gets 30$. Then each chip is worth 30/3.000 = 0,01$. The ICM model assumes, the chance of winning is proportional to a players stack, so a player with 1.500 chips will have an ICM value of 15$, and a player with 500 chips will have an ICM value of 5$.
However most tournaments are not winner takes all. Lets take a simple example like a 10 man SnG, where the winner gets 50%, the runner up 30% and third place 20%. Each player begin with 1.000 chips and buy in for 10$. Now if someone busts another player and dubble up to 2.000 chips, then according to the model they will have twice the chance of anyone else to win the tournament.
However if they win the tournament, they can not contend for second or third place money, and therefore the ICM value of their chips is not 20$. Its 18,XX dollars, which you can calculate at the ICMizer webpage. This basically mean, that if someone open jam in the first hand of the tournament for his 1.000 chips, then you need more than 50% equity against his range to make a profitable call. And as the bubble gets closer, this effect becomes more pronounced.
To some extend its actually rather intuitive. Lets say that 4 of the 10 players are left, someone now have 4.000 chips, someone have 3.000 chips, you have 2.500 chips, and the last guy have 500 chips. Then you obviously dont want to bust, before the guy with 500 chips is either out of there or have chipped up significantly. So in this scenario you need to play in a very conservative way against the two guys, who have most of the chips and only be willing to gamble with the 500 chip guy.