She stopped to have a cigarette.

Literal

She [topic-は] cigarette [object-を] smoke [in order to-ために] came-to-a-halt.

煙草を吸う — literally 'to suck/inhale a cigarette' — is the standard expression for 'to smoke,' just as English uses 'to drink' for 飲む in 'drink soup.' The kanji 煙草 ('smoke-grass') is technically ateji, an ad-hoc kanji spelling for the loanword tabako (from Portuguese tabaco), introduced in the 16th century alongside firearms and Christianity. Today the katakana タバコ is far more common in casual writing. 立ち止まる is a compound verb (stand + stop): 'to come to a stop while standing,' i.e. to halt in your tracks. The pattern verb-dictionary + ために expresses deliberate purpose: 'in order to smoke.'