what is this? Church of the firstborn? Lds?
I'll give a shot at trying to explain some broad outlines of this. But it's not something I know much about -- certainly never spent all that much time thinking about in my day-to-day Mormon life. Others may be able to fill in more details.
I think at its broadest, the Church of the Firstborn is based on the idea that the set of people receiving God's greatest glory in the afterlife (Mormons believe there are various "degrees of glory") is not equivalent to those who are members of the LDS church currently. Instead, those who belong to the Church of the Firstborn are believed to be those who have kept Christ's commandments and their covenants with Him
most faithfully and consistently throughout their lives. So basically, you might say it's Christ's heavenly, rather than earthly church.
This is built on the Biblical reference to Jesus as the "firstborn," and appears more directly linked to the "Church of the Firstborn" in a couple of places in the Doctrine and Covenants (a series of several revelations, codified as scripture, that Mormons believe God gave to Joseph Smith (and a couple others)).
So at its base, it's not that complicated, I think. But when trying to understand how Mormons use the idea, the issue becomes much more complex. It's a term I think most Mormons are familiar with (esp. those who attend Mormon temples), but at the same time, it's not one that LDS people spend a lot of time thinking about in a practical way. It's more sort of the idea, I think, of being a promised blessing in the next life, available to those who have lived especially well and faithfully. The church generally doesn't teach all that much about it and I think most members are satisfied with not worrying about it too much other than as a desired goal, one to be assigned in the next life.
But for those who are especially interested in ideas about Christ's Second Coming, the Church of the Firstborn takes greater significance. I think many of these end-of-day-interested types believe that the Church of the Firstborn will be established on the earth in the build-up to the Second Coming. So from what I've read about the milieu of the groups from which Daybell emerged, many of these people are quite concerned about the details of this establishment of the Church of the Firstborn on earth. And, unsurprisingly, there's a great deal of debate and disagreement among them as to what shape it will take, who will be involved, the role or non-role of the institutional LDS church, when it can be expected, and so on.
So Mike Stroud, who was linked by one poster, might have certain ideas that share a family resemblance to those of Daybell (or Denver Snuffer, another prominent name among these types), but I also think they have disagreements that may make it hard for those who follow one version to fully get on board with someone else who claims to know the true way.
In Daybell's case, it sounds like there may be the sense that the 144,000 are perhaps equivalent to the Church of the Firstborn (though I can't be sure from just the news report). In any case, it does sound like Daybell felt that at this particular time in history, it was important that this "church" be established and its leadership hierarchy strongly identified.
As I've said elsewhere, I have very little clue as to how far along in this process Daybell may feel he is.
They are the ones who are trying to lower their profile as much as possible, IMO. 
