The most common answer I see is something along the lines of "it's the equivalent of liking a post on twitter". It seems that this is not the case, as the Mastodon devs seem rather adamant that they don't want "likes" in Mastodon. Perhaps it's a method of saving posts? Well, that doesn't make sense either, since there is already the ability to "Bookmark" a post to save it.
It really just seems like a "Favorite" is just a bookmark that tells the poster, and the public that you bookmarked the post. And even if this was the reasoning -- which is baffling enough as it is -- it wouldn't make sense since the whole point of boosting something is to tell the public that you like a post.
It really seems like the "Favorite" button has no actual unique purpose. In my honest opinion, Mastodon should just federate "Likes" like normal, and be done with it.
Yeah, from what I'm reading over the git discussion it seems that the favorites are something like a private like verses a public counted vote. If I'm understanding it right it's similar to when people on a lot of corporate chat like MS teams use a 'thumbs up' as kind of an all purpose aknowledgement/approval without actually responding.