It allows you to take an
archetype along with multiclassing instead of choosing between them. No idea how they thought it could be Pathfinder as written.
Uhm. Its a little more complicated than that.
PF2e does not have multiclassing, per se. What it had is Archetypes. Archetypes tie up some of your class feats (for those outside of it, think of them as selectable class features, rather than feats as 3e era+ D&D normally used it) to give you either a set of abilities associated with a different class, or with some sort of specialized offshoot or maybe an extension of your class. I'd describe the latter as the PF2e version of Prestige Classes.
But they do tie up class feats to do so. And class feats are normally the most valuable of the three kinds of feats (Class/General/Skill) you can take in PF2e, and you only get so many of them. So normally to get an Archetype costs you some significant amount of capability in your main class.
Free Archetype allows you to take the Archetype feats associated with one archetype for free as you get to the levels when they're available (often there's only one feat at each of these levels that makes these available--I want to say there's about five available across the 20th level range, but don't hold me to it).
So in practice (assuming you don't just take some of the early Archetype feats and call it good), the difference is you normally are in something like the choice between being fully functional in your class, multiclassing, or taking a prestige class. Free Archetype essentially allows you to do two (since there's nothing stopping you from still sacrificing those class feats for a
second Archetype). Most of these combinations are far less strong that tossing on a lot of the old Multiclassing/PrCs would have been (though you can still get some strong synergies in a few cases--a lot of fighting types can get some pretty nice juice out of taking the Rogue Archetype as their freebie for example).