So the LDS Church has previously published 11 essays about various theological/historical issues involving the church, including violence by and against early Mormons, polygamy, the Book of Mormon, the idea of man becoming like God, etc. Well, now the Church has finished and published
the last two essays, which detail with the topics of Heavenly Mother and LDS women and the LDS priesthood respectively. I'll give a quick synopsis in case anyone can't access the essays.
1.
Women and the priesthood. This one is longer by far than most of the other essays, and of course it deals with the issue of women's ordination (or lack thereof) in the LDS Church. First, the essay details the many things women can do in the church, teach, serve missions, perform temple rites, lead auxiliary organizations, etc.
It goes on to say that when Mormonism was organized, most churches had men-only religious leadership, and that Mormonism was no different. However, in the LDS church, religious authority is theoretically through laymen, that is, not professional or inherited. The essay goes on to detail what the priesthood means, and what it authorizes its holders to do.
It goes on to explain the Relief Society, the women's auxiliary organization in the church and how it was formed. Of note is that the essay clarifies that though Joseph Smith "ordained" women to Relief Society positions and gave them the metaphorical "keys" of authority (usually terms associated with the all-male priesthood), that doesn't mean that he ordained them to any priesthood office.
After explaining that, it goes on to talk about healing blessings and laying on of hands, which is a common priesthood activity in the church. Basically, a priesthood holder (or two or more) will put his hands on your head and pray over you. It's not as weird as it sounds, there's no "BE HEALED" shouting or forcible holding someone down or whatever. Anyway, apparently early LDS women also did this, but didn't utilize the priesthood in doing so, and just used normal faith. Joseph Smith thought this was a-okay, and endorsed it. LDS Women slowly stopped doing healing blessings past Brigham Young, and nowadays don't do it at all. Though it never says that they can't, just that they don't.
2.
Heavenly Mother. A very short essay, mainly because we don't actually have much doctrine about Heavenly Mother, other than that she's the wife of God the Father (who is separate from Jesus Christ in LDS theology as we are not Trinetarian), and the spiritual mother of all humanity (as opposed to a physical mother). Basically, the idea is that if we have a Father in Heaven, why not a Mother? We don't pray to her, and not much is known about her personality. Church leaders have said that not much is revealed through divine inspiration because God doesn't want humanity to mock and belittle Heavenly Mother like they do to him and Jesus Christ.
My thoughts on all of this is that I'd like to see more about these issues and that I feel that the explanation that women didn't use the priesthood despite doing a modern priesthood activity is a bit mealy-mouthed. I do hope that Heavenly Mother is explained more in detail, however.
Also, these particular essays have gone up after years of pro-LDS women's ordination group Ordain Women have been raising a fuss about these issues. So it's pretty clearly a response.