A quotable remark is one people want to say again — interesting, clever, or funny enough to write down or repeat. A politician hopes for a quotable line on television; a teacher might smile and say a student gave a quotable answer. Though actually, if you only look at the pieces, quote + able looks like “you are allowed to quote it.” In real use it almost always means “worth quoting,” not “permitted to quote.” A dull true sentence can be quoted; a quotable one is the one people remember. It is used of remarks, lines, phrases, interviews — the bits that travel.