Originally I smoked, [but] now I don't smoke.
抽烟 is an example of a separable verb (离合词), which combines two words: the first word is a verb 抽 and the second word 烟 is its object (hence they're also called "verb-object phrases"). Here, 抽 doesn't necessarily need to take an object, and can be omitted.
Thus it's more analogous to saying:
Originally I smoked (抽) tobacco (烟), but now I don't smoke (抽).
Sometimes separable verbs are easily understood, e.g. in 吃饭 = "to eat a meal", 吃 is "to eat" and 饭 refers to the meal, or in 打篮球 = "to play basketball", where it's clear that 打 is the verb and 篮球 is its object. However, in some cases, the object in a separable verb is somewhat abstract (like in 游泳).
For 抽烟, the object 烟 is tangible: it's the thing that is being smoked (likely tobacco).
[In English, there are comparable phrases, like "I ran a run" or "I danced a dance". (Or even: Waiting for a king to apologize, one can wait a rather long wait.)]
Textbooks often list separable verb vocabulary, such as 游泳 and 跑步, as if they were single words (and identify them as separable verbs in some way, such as writing: yóu//yǒng). Sometimes they are better thought of as two separate words (verb + noun) with a strong collocation (i.e., they often go together). So 抽 is a verb, 烟 is not a verb (it's a noun), and a textbook probably lists 抽烟 as a single word for simplicity (since 抽 and 烟 both have other meanings).