memorize, recite from memory
諳 centers on internalizing words so deeply that they can be spoken from memory: memorizing and reciting without looking.
諳 combines 言 (speech) with 音 (sound), suggesting speaking from memory or reciting aloud. The exact historical development is uncertain, but the component relationship is clear.
Words 言 and sound 音 together: imagine a performer reciting a long poem flawlessly, the words flowing as naturally as a familiar melody.
For アン, picture an announcer reciting a memorized script: announcer -> アン, and the words come out perfectly from memory.