Free space is what we’ve always known it to be. It’s space on disk where there’s nothing, that’s ready to have data poured into it. Purgeable space is different. Purgeable space is a collection of files that are really on disk, ready to be read or modified or added to at any time—stuff like files stored in iCloud, dictionaries you haven’t used recently, certain large fonts (especially of Asian languages) that you may never or rarely use, movies and TV shows you’ve already watched (and are re-downloadable from iTunes), and photos and videos in that are synced with iCloud Photo Library (if the Optimize Mac Storage setting is turned on in Photos preferences).
These are real files, but Apple considers them expendable. They can be deleted immediately, without warning, in order to free up disk space, because they can always be downloaded again later.
I don’t remember hearing about the handling of purgeable space when Sierra was launched, but that’s okay. Most users won’t notice anything different going on under the hood; MacOS will, probably, just do the right thing.