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.
The issue is that favorites are a mastodon-specific thing. Mastodon does not federate actual "likes". So, if mastodon users actually do want "likes", then they should federate them the same as everyone else. The "favourite", on it's own, is otherwise pointless, and redundant.
This is part of my point though. Why make a separate "Like" feature that doesn't integrate with the existing infrastructure for the exact same thing? If people are treating it as a "Like", then why not actually make it a "Like"...?