Listen to this piece of music, "God Save the Queen," the national anthem of the United Kingdom:
https://www.youtube.com/watch?v=tN9EC3Gy6Nk
To people in the Western European musical tradition, this music contains a series of harmonies that give a sense of tension, and a sense of progress, as if we were somehow "moving." At about 0:22, we reach a chord which gives a sense of rest, relaxation, and stability. The "tension" of the preceding chord progression has been "resolved." The musical problem has been solved, it feels as if the chords have ended up in the right place, where they ought to be.
It's not quite as obvious to me here, in the national anthem of Saudi Arabia as played at the Olympics, but nevertheless I hear it at about 0:10, 0:20 and other places. The harmony progression stops moving and reaches a natural position of rest. It "resolves."
https://www.youtube.com/watch?v=wEs90t7XooA
I'm not sure what is meant by saying "jazz music doesn't resolve," but I suppose it depends on the particular jazz style. As for "God doesn't resolve" I guess it just means life flows on; in the words of a song by Harry Chapin, "no clear-cut beginnings, so far no dead ends."