Chotto (ちょっと) means “a little” or “a bit” — and, said with your voice trailing off, it is the politest way to say no.
You ask a Japanese friend if they're free on Saturday. They say 「どようびは、ちょっと…」 and stop. You wait for the rest of the sentence. It is not coming — because that was the whole answer, and the answer was no.
The sentence is left unfinished on purpose
Textbooks teach ちょっと as “a little”. That is true, but it is not the most important use. Its most important job is to start a refusal that you never finish. The listener completes it in their head — 「ちょっと つごうが わるいです」 (it's a little inconvenient) — so nobody has to say “no” directly.
This is why Japanese conversation can feel soft and indirect. A plain 「いいえ」 to an invitation can sound too strong; ちょっと lets someone say no without hurting the friendship. If you hear it, accept the “no” politely and change the subject — asking “why?” is what would be rude.
Its other jobs
It softens anything you're about to say: 「ちょっと たかいです」 (it's a bit expensive) is a complaint that sounds less harsh. It's also how you get someone's attention — 「ちょっと すみません」 — and how you ask for a moment: 「ちょっと まって ください」, which you will learn in Chapter 7 of the course (“Please wait”).
あした、えいがを みませんか。
Would you like to see a film tomorrow?
あしたは、ちょっと…
Tomorrow is… a little…
わかりました！
Understood!
Can you use it?
Yes, and it is a quick way to sound more natural. When you can't accept an invitation, say the day, then ちょっと, then stop. You don't need an excuse — making one up sounds less honest than simply stopping. The only trap is your tone: said quickly and sharply it can sound annoyed, so say it softly, as if you are sorry.