The adverb subtly describes something that's done in a delicate or understated way. You could subtly suggest to your best friend that a breath mint might taste good, rather than telling her straight out that she's got terrible breath.
When you do something subtly, you do it quietly and indirectly — like subtly criticizing your mom's choice of beachwear. If you smile subtly, it's a small, mysterious, Mona Lisa-type smile rather than a wide, open one. There are two tricks to the word subtly: first, when you add the ly to the word subtle, the e gets dropped. Second, don't confuse subtly with subtlety, a noun meaning "the state of being subtle."