If your friend invites you out somewhere, you can demur by saying いえ、ちょっと which implies you don't want to go out, without specifying the reason. Its more polite than saying, "I don't want to go out" or "I don't want to do that thing".
Your acquaintance is showing you a kindness, and it would be rude to just reject it by saying "I'm not interested". So instead you just decline by いえ、ちょっと (implying that you are busy on that day).
But this requires a pretty good degree of fluency to just toss out this phrase and have it be accepted. Also, your friend might continue to push you and ask you why you can't make it.
Or, if you are out eating with friends, and they ask you if you like (for example) sushi. If you don't like sushi, you can say,
いえ、ちょっと, again, implying you don't like it in a roundabout way. Its more polite than saying いえ、きらいです which would be a logical and acceptable answer in English - but in Japanese it feels harsh and could be rude depending on the context.