Each area has gates players can activate, Dengeki PlayStation explains. Once these are turned on, Serah and Noel can travel to different periods by standing on a gate. Some areas have multiple gates to trigger. You will use these to find out of place artifacts, which your moogle can use. Gates only stay open for a limited amount of time, but players can reopen them if time runs out.
It sounds like collecting parts is a core part of Final Fantasy XIII-2. The magazine has a screenshots of Bresha Ruins, which says "Fragment 0/8." Another screenshot shows Bresha Ruins through time where in the beginning of Final Fantasy XIII-2 (AF 005) it’s lush and brimming with life. At AF300, the area is in ruins.
Serah’s search for Lightning is the heart of the story and Lightning is in Valhalla. She’s a guarding Etro’s temple as a knight and fighting Chaos Bahamut. Noel, the new character who travels with Serah, met Lightning. His goal is to change the future. For more about Noel’s past, read this post.