refined, elegant, skilled
嫺 centers on cultivated grace and ability: being refined, elegant, and skilled, often with a feminine connotation from the woman radical.
嫺 combines 女 (woman) with 閒, which likely contributes the sound and carries a sense of leisure or refinement. The exact historical development is uncertain.
A woman 女 beside 閒, which suggests a calm, orderly space. Picture a refined woman in an elegant room, demonstrating her skilled grace.
For カン, imagine a can of polish used by the elegant woman to refine her surroundings: can -> カン, and her skilled touch makes everything shine.