The acronym summarizing Calvinist theology is TULIP, the "I" standing for Irresistible grace. This means that if God offers his grace to someone, it overwhelms them and they cannot help but accept it. A large part of the reason for this doctrine is that if God's grace is resistible, it would mean that our eternal destinies are ultimately in our hands rather than God's. This would mean that we essentially save ourselves. This isn't meant to imply that we can do it without God, but it does mean that God can't (or at least doesn't) do it without us. Ultimately, whether the individual goes to heaven or hell rests in his decision to accept God's grace or reject it, not on God's decision to save him.
This is allegedly intolerable for several reasons. Here I'll just focus on the fact that traditionally Christianity has emphasized that initial salvation (and grace in general) is entirely from God's side, and there's nothing we contribute to it. We can't ask to be saved or even want to be saved unless God bestows his grace upon us. To deny this is to accept a form of Pelagianism or at least Semipelagianism -- heresies that have been condemned by virtually all branches of Christianity throughout history. In order to avoid this, we have to say that our salvation is out of our hands; it must be wholly in the hands of the Holy
I'm not convinced that the Calvinist rejection of human choice in salvation is accurate. The analogy I tend to use to think of this is that of a drowning man. If you're drowning and someone swims out to rescue you, would you say that you are participating in your own rescue by not fighting off your rescuer? I mean, you could: ultimately it's your decision whether you let the other person rescue you, right? The final choice is yours. But to say that you're participating in your rescue, that ultimately you're rescuing yourself, strikes me as obviously false. By allowing yourself to be rescued you are not doing anything active, it's entirely passive. And I think this holds for the individual who is offered God's grace: accepting means that you stop doing whatever you're doing and let God save you. Only by rejecting him are you doing something active ("fighting him off").
Of course, this parallel only goes so far; there are some obvious dissimilarities. A drowning man doesn't only become aware that he is drowning when a rescuer reaches him. A drowning man doesn't have temptations to make his rescue appear less attractive. A drowning man may fight off his rescuer out of pure panic rather than a rejection of being rescued. Nevertheless, I think it does parallel the situation sufficiently to show that the Calvinist concern about grace being resisitible is unfounded.