Today it is accepted that one may smoke on Yomtov (if you light up from a pre-existing flame — one may not kindle a fire on Yomtov.) But historically many authorities did not allow it and it is at least questionable whether it should be permitted today.
Allowing smoking is based on an extension of the permission to cook on Yomtov. The main difference between Shabbat and Yomtov is that on the latter one may do some of the categories of work necessary to prepare food. From this, it was allowed to use an existing fire for other physical pleasures, for example to heat up water to wash with.
The Magen Avraham (17th century) was among those who disagreed with adding smoking to this list as smoking was only a minority pleasure and therefore did not justify suspending the prohibition on using fire. And that, was before we knew that smoking kills you and should probably be forbidden for that reason.
Rabbi Julian Sinclair