Seeing a representation of something visually often helps us to understand it better. I have reproduced some diagrams I found helpful. The first two are from Grudem and demonstrate forgiveness of sins and the imputation of Christ’s righteousness to us. The last is from Sproul. It illustrates our union with Christ and how this functions in relation to imputation.
Justification: Imputation of Christ’s Righteousness to Us
(AN ILLUSTRATION OF JUSTIFICATION BY FAITH)
 Wayne Grudem, Systematic Theology: An Introduction to Bible Doctrine (Grand Rapids, MI: Zondervan, 1994), 725 and Sproul, Essential Truths, 190.
 Sproul, Essential Truths, 190.