To be lucky; to have good luck—colloquial form of 'ついている' used frequently in conversation.
今日はいろいろラッキーだね。本当にツイてるよ！
You're having a lucky day—you're really on a roll!
宝くじで少し当たって、最近ついてる気がする。
I won a little on the lottery; I feel lucky lately.
彼は試験に受かってついてるね。
He passed the exam—lucky him.
To be attached, included, or to have something accompanying it—meaning that something is physically attached or comes along.
このスマホには充電器が付いているか確認してください。
Please check whether this smartphone comes with a charger.
説明書が箱の底に付いているのを見つけた。
I found the manual attached to the bottom of the box.
新しいソフトには便利な機能がいくつか付いている。
The new software has several useful features included.