This rare kanji has no clear standalone meaning. Treat its meaning as uncertain.
晻 combines 日 (sun) with 奄, which likely contributes the sound. The exact historical development is uncertain.
The sun 日 is covered by 奄, suggesting darkness or dimness. Picture the sun being obscured, leaving everything in shadow.
For アン, imagine an unlit room where the sun is blocked: unlit -> アン, and the darkness matches the obscured sun in 晻.