Detachment from sin refers to making the conscience decision to reject one's desire to sin (especially habitual sins), This does not mean one does not sin anymore (due to one's weakness in temptations), but that one has decided to fight against sin instead of accepting (attachment to) sin.
The struggle against sin will always be with us and sometimes we may fall, but we get back up and continue the fight never accepting sin, large or small. This is detachment from sin.
Remember that detachment from sin is a conscious decision. We have to work on identifying all our attachments to sin (all sinful habits) large and small. Ask for God's grace to detach ourselves from our sins. Making the conscious decision to reject sin is a giant step, however, working to detach (break the habit) from all our sins may take many small steps.
In doing this, if not for the love of God, we learn to love God more and more.
"For the wages of sin is death. But the grace of God, life everlasting, in Christ Jesus our Lord." - Romans 6:23
"If someone should try to persuade you of any lax doctrine, do not believe in it nor embrace it; even though he might confirm it with miracles. But believe in and embrace more penance and detachment from all things, and do not seek Christ without the cross." - St. John of the Cross
"After you have made a decision that is pleasing to God, the Devil may try to make you have second thoughts. Intensify your prayer time, meditation, and good deeds. For if Satan's temptations merely cause you to increase your efforts to grow in holiness, he'll have an incentive to leave you alone." - St Ignatius of Loyola