to cover: to lay something over a thing so that what is underneath is shielded, swallowed from sight, or kept from being known.
The picture behind this verb is a simple one: something comes down on top of something else until the thing underneath can no longer be seen. Waves close over a boat in a storm, a jar is set over a burning lamp, and terrified people beg the hills to fall on them and cover them. In every case a covering arrives from above, and the covering itself is what the word keeps in view. Its nearest neighbor, the ordinary verb for hiding (κρύπτω), works the other way round, moving a thing out of sight rather than laying a layer over it.
From there the word moves easily to whatever is kept from being known. Jesus promises that nothing covered will stay covered, and Paul says that if the good news he preaches is veiled, it is veiled only among those who are perishing. The covering now lies over a mind rather than over an object. It is also never presented as permanent: the matching verb for taking a covering off (ἀποκαλύπτω) stands right beside it in the promise that what is hidden will be uncovered.
The third use comes straight out of the Old Testament, where a wrong can be covered so that it no longer stands against a person (the Hebrew verb is כָּסָה). Both James and Peter use this Greek verb in exactly that way when they say that love, and bringing a wanderer back, "covers a multitude of sins." A compound of the same verb (ἐπικαλύπτω) carries the identical idea in Paul's quotation of the psalm about the person whose sins are covered.
What holds the three uses together is that a covering always stands between something and the eyes that would otherwise see it: water over a hull, a lid over a flame, unbelief over a message, mercy over a wrong.