I've been using WP Super Cache for months, but only today have I finally figured out what this option does. The wording for it, although grammatically correct, is unidiomatic and therefore confusing to native English speakers. In particular, the placement of the word "only" in front of the verb gives the wrong impression of what is happening. Moreover, using the term "current page" makes it sound like it's the most recent post being updated (or not), rather than the home page. I have unchecked this box repeatedly over the past few months, only to find out to my dismay that my home page was not updating when new articles were posted.
I cordially recommend changing the wording to "Refresh home page only when comments are made" to alleviate some of the confusion.
However, given the fact that this is in fact exactly the opposite of what really happens (when the box is checked, the home page is not updated by comments), I think the wording should actually be "Refresh home page only when new post or page is published." Then there would be no confusion.