Definition of chip count
A chip count is when a player asks the dealer or tournament director to find out the exact value of an opponent's stack (how many chips he has). This situation only occurs when playing live (online, we know quickly at any time the size of our opponents' stacks). The chip count usually occurs late in tournaments when the situation becomes difficult.
Why do we need a chip count?
Usually, the player calling for a chip count has a tough decision to make. If a player is all in before me and I have aces, I don't need to know how big his all in is, I call the bet! But let's imagine the following situation. You are at the final table of a tournament. You are the chip leader on the table. You are very active and you make a lot of 3bets and raises. A player opens in early position, you are on the button with AQ and you go for a 3bet. The player says: "I'm all in". Here, you will ask for a chip count. You are the chip leader and your stack is valuable, but if what he adds in chips after your raise is very small, you have no choice but to call the all in. You need to know the size of his stack to make the right decision.