One aspect of the restoration was expressed by Nephi in his vision, in which he describes many plain and precious truths that will be lost during the ages. If one looks at Joseph's teachings, there is one, I would argue, that stands out most clearly as such a restoration. It is one we talk about but don't emphasize too much. Ironically enough, it is not one that Nephi, nor the entire Book of Mormon even addresses. But as a testament, not only of Jesus Christ, but of Joseph's mission as prophet, seer, and revelator, the Book still sets the stage.
I am referring, of course, to the restoration of the plurality of Gods. Of all Joseph's teachings, this remains perhaps one of the most radical. It is also one of the most outstanding, in that it preceeded any significant research on the subject of the Israelites ancient beliefs by over one hundred years. It doesn't take too much digging to find the wide swath of historians who will agree (there are, of course, those who do not) that the ancient Israelites were not the monotheists of lore, but polytheists. Polytheists who believed in a pantheon of gods, a Council in Heavan, so to speak, overseen by a Most High God. Some even argue that the development of Yahweh Elohim (the LORD God) was a merging of two Gods, a Father and Son, and that the merger was not complete in some segments until even after Jesus Christ, with some holding a view that Yahweh Elohim was God and that he was served by the Angel of the Lord, a sort of secondary deity. This is perhaps what allowed Jesus to be accept so readily (by a least a portion); there was many who could see in Jesus' messiahship this very aspect of the "Other God", so to speak. Of course, the other part of this pantheon is the female deities, the Goddess wives of the God husbands, the most well known name wise being Asherah, the Queen of Heaven. An idea, of course, which Joseph also restored in laying the foundation for discussion (what little we have) of our Mother in Heaven.
What I find particularly interesting about this particular branch of the restoration is that, as I said above (and would say better, with footnotes and whatnot, were I not so lazy) is that this is perhaps the clearest example of Joseph restoring a clearly ancient idea without any real preceding foundation. There is not equivalent to Swedenbourg's three heavens, or to the Masons' ceremony, or even the Kabbalists Tree of Life (I'm not saying necessary arguing this things were the source of even the inspiration for Joseph, only that they had a potential role). I think you would be hard pressed to find any meaningful source for the Council of the Gods in Joseph's environment. And certainly, as I mentioned, not scholar who would be talking about it for another century. Yet there it is, from as early as Section 76 in the D&C, and finally so bold put forward in Joseph's last sermons, the King Follett discourse and the Sermon in the Grove. I'm not saying "and this proves Joseph was a prophet". No testimony should be based on such ideas. Nevertheless, there it is, begging to be explained, how his relatively uneducated man came forward with such a bold and blasphemous idea. Even more, how he could be so right.
It does to me emphasize the importance of a prophet, however. All these scholars have written all these books about it. Yet not one is able to step forward and say "And this is the truth about God(s)!". Yet Joseph was, and did.
The other irony, of course, is how little we appreciate it. How little we do with it. Joseph taught it so boldly, so defiantly, and it impacted Mormonism quite significantly early on. Not so much now. Of course, of itself that isn't a problem and it certainly isn't my place to say what should and shouldn't be emphasized, and there are all the easy arguments, and all the good ones too, about why we choose not to. But the irony remains - if we are going to make such a big deal about the restoration, not just of authority, but of plain and precious truths as well, that we wouldn't make more of one of the clearest restorations of such truths Joseph gave us.
Some scriptures of note
D&C 76:58 (incidentally, while this verse specifically refers to sons of God, I think the context obviously implies daughters as well, particularly verse 24)
In the end, it seems to me that we are, as a whole, very uncomfortable with the idea of the plurality of gods. Perhaps it makes us feel too "outside the mainstream". But the discomfort is obvious. I just can't quite grasp why...