Calling is the simple act of meeting another player's bet in order to stay in the hand and continue competing for the pot.
There are a number of reasons why you might call, but they all come down to the same premise: you want to stay in the hand. Maybe you have the best hand, maybe you have a good draw, or maybe you are planning to bluff later either way, if you think you can win the pot, you can call in order to stay in the hand.
Remember, always call when action is on you--otherwise, you might be giving free information to another opponent who is only thinking about calling.
And, as always: verbal actions are binding. This means if you say "Call," but then put in the wrong number of chips, you're obligated to meet the bet--even if you thought it was less than what you anticipated. On the other hand, if you call and put in too much, you get those chips back. Always make sure you know the bet amount before calling!
Sometimes, you want to call, but don't have the right denomination of chip to do so for instance, the bet is $1, but you only have $5 chips. In this instance, you can make change. At casinos, you might have to let the dealer make the change, whereas at home games you might be comfortable throwing the chip into the pot and taking out the correct amount yourself. Regardless, always announce "Call" before making change--otherwise, you could get dinged on a string bet, and end up being obligated to leave your last chip in the pot!