Daijoubu (だいじょうぶ) means “all right”, “OK” or “no problem” — and in shops it often means “no, thank you”.
Someone trips on the stairs. Everyone turns: だいじょうぶ？ It may be the most comforting word in anime — and it hides one trap that catches almost every learner in a Japanese shop.
The basic meaning: all right
だいじょうぶ means “all right, safe, no problem”. As a question it asks whether someone is OK. As an answer it says that you are.
Between friends you drop です: だいじょうぶ？ — だいじょうぶ。 Say it twice, だいじょうぶ、だいじょうぶ, and you are reassuring someone: “it's fine, it's fine.”
The trap: “I'm fine” as “no, thank you”
In shops and restaurants, だいじょうぶです is today's soft way to turn something down. The idea is “I'm fine without it.”
ふくろは いりますか。
Would you like a bag?
だいじょうぶです。
No, thank you. (I'm fine.)
So if you answer だいじょうぶです when you DO want the bag, you won't get one. To accept, say はい、おねがいします (“yes, please”). To refuse clearly, add いいえ: いいえ、だいじょうぶです.
Can you use it?
Constantly. だいじょうぶですか is the kind thing to say when someone drops something, looks lost or seems unwell, and だいじょうぶです is the polite way to say you need no help. Just keep the shop meaning in mind.