The First Order is a neo-Imperial loyalist junta existing in the Outer Rim that signed on to the Galactic Concordance, preventing it from officially rearming beyond some acceptable level or from building new weapons. Obviously the FO doesn't care about this and is secretly building top of the line TIE Fighters and Resurgent-class Star Destroyers, although how they get these resources isn't talked about. In Finn's section, however, we know that the FO views itself as the defender of galactic stability and civilization and thinks of the Republic as a bunch of weak degenerates who have allowed piracy, gangsterism, and - interestingly - alien invasions increase, so I wonder if that means we're going to get something like the Nagai-Tof, Ssi-Ruk, or Yuuzhan Vong back in the canon.
Anyway, galactic borders are strictly defined, and even though the FO keeps encroaching on NR territory the NR refuses to respond unless there is some sort of act of open warfare. Poe originally serves in the NR Navy and when he's on a scouting mission he stumbles onto the FO attacking and capturing, the Yissina Zyde. When he returns to base he asks permission to investigate but is not allowed because of orders from on high (although Poe doesn't know if this means from the Senate or military high command). Poe and the commanding officer argue about whether the FO should be confronted more directly, with the officer saying that there are "rumors" of the Resistance countering them. Poe decides to risk a court martial anyway and goes out by himself, eventually finding the Zyde and learning that it contained materials that could be useful for building turbolasers, so he speculates that the FO captured it for its resources. When he returns to base he expects to be scolded but instead ends up being taken away in secret by Major Ematt who brings him to a meeting with Leia, who recruits Poe to the Resistance (she asks him at one point if he's heard of the Resistance and he tells her that he has heard there are elements of the military who are disgruntled with the Senate's policy, so they split off and formed their own organization; Leia tells him this is "mostly true").
Poe then spends some time working in the Resistance, going around and recruiting other people. Most of the Resistance top brass are ex-Rebels, with Leia having been shunned by the NR government for being an "alarmist" about the FO, but at this point the Resistance is still not openly fighting with the FO - their goal instead is to gather evidence of FO criminality to present it to the Senate, which would tie in with the deleted scene of Kor Sella being sent by Leia to Hosnian Prime. Anyway, they learn that there is a senator who is a traitor supplying information to the FO and Poe is sent on a mission to capture the Senator's yacht so he can download the information from it, but the mission goes wrong when he gets ambushed by FO ships. He still manages to get away with the data, which points to the location of Lor San Tekka, who Leia has been looking for.