K-p-r is more than a physical cover, even though it seems to have that sense in the story of No’ach: God tells him to make an ark, v’chafarta otah mibayit umichutz bakofer (Gen. 6:14). This could possibly mean “you shall cover it inside and out with a cover”, but the needs of that ark went beyond any ordinary cover, hence the rendering “you shall coat it inside and out with pitch”, the purpose being to make the ark waterproof.
Ibn Ezra links kapporet with kofer, “a ransom” (as in Ex. 21:30, a verse in Parashat Mishpatim). In this way the kapporet becomes more than just a cover but has a propitiatory or atonement role in the people’s spiritual life.
How this links up with the idea of a cover is that when one achieves Divine forgiveness, the Almighty covers over our sins and, as it were, eradicates their traces. On this basis Yom Kippur is the day when our transgressions are no longer visible.