Something that's phonic is related to spoken words or sounds. Puns often rely on phonic similarities between words — like when you declare that the panda at the zoo has "the right to bear arms."
In its singular form, phonic is generally used as a synonym for phonetic — both words describe the sounds of speech. The phonic elements of poetry are much clearer when it's read out loud, while the phonic variations between words in a foreign language can be tricky to distinguish from each other when you're just starting to learn it. Add an s and you get phonics, a method of teaching reading by sounding out letters.