So you can be anywhere inside a quote and do "change inside quotemark" and it'll delete everything inside and leave you in insert mode. "around" would delete everything inside and the quotemarks.
These can be used with other things, parentheses, square brackets (and I think some plugins extend it to html tags and the like).
Of course, you can swap out c for d, y or any of the other verbs.
Working in clojure and deleting everything inside a particular level of nested parentheses is awesome.