The following syllogism by John Owen (1616-1683) forms an easy way to understand and explain what we mean by Limited Atonement – the extent of the atonement made by Jesus Christ via His death upon the cross.  The author also gives a defense against the false teaching that belief is necessary to cause the atonement to be effectual for the person, or that unbelief is a sin for which Christ did not atone (i.e. an unforgivable sin).

FOR WHOM DID CHRIST DIE?
John Owen

The Father imposed His wrath due unto, and the Son underwent punishment for, either:

All the sins of all men.

All the sins of some men, or

Some of the sins of all men.

In which case it may be said:

That if the last be true, all men have some sins to answer for, and so, none are saved.

That if the second be true, then Christ, in their stead suffered for all the sins of all the elect in the whole world, and this is the truth.

But if the first be the case, why are not all men free from the punishment due unto their sins?

You answer, “Because of unbelief.”

I ask, Is this unbelief a sin, or is it not? If it be, then Christ suffered the punishment due unto it, or He did not. If He did, why must that hinder them more than their other sins for which He died? If He did not, He did not die for all their sins!”