Learn Russian: Здесь нет курящих, поэтому воздух чистый. - There are no smokers here, so the air is clean.

It is a substantivized participle—a participle that has taken on the role of a noun. It comes from the present active participle курящий (smoking). While it literally means 'smoking people', it functions in this sentence exactly like the noun 'smokers'.

Why is курящих in the genitive plural?

The word нет (when used to mean 'there is/are no') always requires the following noun or pronoun to be in the genitive case. Because the sentence refers to a general absence of multiple smokers, it takes the genitive plural form of курящие.

Could I use the regular noun курильщиков instead of the participle курящих?

Yes, Здесь нет курильщиков means exactly the same thing. However, using the substantivized participle курящих sounds slightly more formal or official, which perfectly fits the context of public rules, signage, or designated non-smoking spaces.

Why use the full adjective чистый instead of the short form чист at the end of the sentence?

While you can use short-form adjectives for predicates (воздух чист), the full form чистый is much more common in everyday spoken Russian to state a simple, everyday fact. The short form here would sound a bit too elevated, poetic, or dramatic for a casual explanation about a room's air quality.