Transgressions are compared to a cloud that form a barrier between a person and heaven, where God dwells. The transgressions will completely disappear, just as a cloud evaporates without leaving a trace.
When the prophet wishes to bring the tidings of redemption to Israel, he uses the simile: "I erased your transgressions like a thick cloud, and like a cloud have I erased your sins; return to Me for I have redeemed you." (Isa. 44:22). Sins and transgressions are described as recordings in God's Book of Remembrance, and when a person is forgiven, they are erased. However, a mark is often left, as a reminder that something had been written prior to being erased. This is why the prophet uses the simile of a cloud. Looking up at a clear sky, it is often difficult to believe that, just a short while ago, it had been an overcast, cloudy sky. Therefore the prophet assures us that God will erase Israel's sins, without leaving any trace of the transgression. Furthermore, sins are like black stains on Israel's character, just like clouds appear to be black stains in the sky. God will remove Israel's stains and purify them, just as the sky looks clear after the clouds have blown away.
Sins are like a barrier separating Israel from God. As the prophet says elsewhere: "But your iniquities were separating between you and between your God" (Isa. 59:2). This is symbolized by clouds which prevent Israel from seeing the heavens where, figuratively speaking, God dwells and from where He looks down on earth. When Israel sin, God turns His face away from them, as if there was a barrier of cloud between them, preventing their prayers from ascending up to Him. In Eicha, the prophet laments: "You have enveloped Yourself in a cloud, so that no prayer can pass through." (3:44) Now that the sins have been forgiven, the cloud has been obliterated and Israel can once again come close to God, without any barrier separating them. So, the prophet continues: "Return to Me for I have redeemed you."
The term 'redemption' is used when a person who has been sold into slavery is redeemed and released. Because of their sins, Israel were sold to the nations: "You were sold because of your transgressions." (Isa. 50:1) and now, once the sins have been erased, the bill of sale has been torn up. The nation of Israel has been redeemed from slavery and now return to the true Master, to God.