What happens when I close a gate?

An open gate is one that you've found in-game and used a fragment to activate. Open gates save your progress as you roam about, and as you leave them to return to the Hisoria Crux.

Some portals have the close gate option. When you close a gate it resets all of the events and content there (other than collecting fragments and key items). This is so that you can re-play the area to make different story-altering live event choices. Those portals that do not have a close gate option don't have multiple story lines to choose from. You can still go back to collect missed items, but there's only one outcome from completing that time period.

This is what you're expected to do in order to experience each of the anomalies for a gate that has many of them. It is also how you earn the Anomalous trophy / achievement.