The ending of Insidious: Chapter 2 destroys Michelle's spirit, returns Josh to his own body, and has Carl hypnotize Josh and Dalton so they forget the spirit world. The family seems safe and reunited. In the final scene, Specs and Tucker investigate another case, a young girl in a coma. Elise's spirit appears in her room and sees something unseen behind the child, which sets up a further story.
So, what does the ending actually resolve? The haunting of the Lamberts is tied to Parker Crane and his mother, and with Michelle gone the specific threat to the house ends. The Bride in Black, which the 1986 flashback presents as a woman, turns out to be Parker. In my opinion, that reveal is the film's cleverest piece of rewiring, because it recasts the scares of the first act as something with a human history behind it.
The forced forgetting is the part I find most interesting. Elise suppressed young Josh's ability and altered his memories in 1986, and Carl now does the same to Josh and Dalton. It could be argued that the family is given peace by the same method that caused the problem. Insidious: The Red Door later picks up nine years on, with Josh having buried his memories of the Further.
The last scene with Elise is the sequel hook. She appears as a spirit watching over the living, and perhaps the something unseen behind the girl suggests the Further has more to show. To see where that thread continues, the Insidious movies in order page lays out where to go next, and the Further page explains the spirit world itself.