To proceed with the story, look for the event icons. This helpful icon will appear in your main map, minimap, and you'll find it in the actual spot where it is marked in the map. If you need to talk to certain characters to trigger the story, you'll see the icon over their heads. Remember that you can proceed in the game at your own pace so you don't really need to proceed with the story unless it's blocking your progress in exploring new areas in the game.
You can also backtrack some of the recent logs in case you want to review it. It contains helpful information that you may miss during Combat like the growth of your weapon proficiency, dropped items, etc.