What exactly is meant by attachment to sin? How is it different from plain old temptation?
A standard temptation to a particular immoral action can afflict anyone. If a person has never before committed that sin, he is usually able to resist the temptation should he choose to do so. But once he has committed that sin, his ability to resist committing it weakens and it becomes a problematic area in his life.
For example, someone who has never told a lie will not only find it difficult to lie, he will also find it easier to resist the temptation to lie. But once he starts lying, he will not only find lying easier, he will also find it more difficult to tell the truth. Thus he becomes “attached” to the sin of lying. Freeing oneself from such attachments is difficult because we must struggle hard to re-orient ourselves to choosing the moral option.
To understand this doctrine and practice of the Church [indulgences], it is necessary to understand that sin has a double consequence. Grave sin deprives us of communion with God and therefore makes us incapable of eternal life, the privation of which is called the “eternal punishment” of sin. On the other hand every sin, even venial, entails an unhealthy attachment to creatures, which must be purified either here on earth, or after death in the state called purgatory. This purification frees one from what is called the “temporal punishment” of sin. These two punishments must not be conceived of as a kind of vengeance inflicted by God from without, but as following from the very nature of sin. A conversion which proceeds from a fervent charity can attain the complete purification of the sinner in such a way that no punishment would remain (CCC 1472, emphasis added).