I've seen various people on this forum say that they like to go exploring in MMORPGs. If that means go look at the artwork but don't get anything for it, then there's nothing wrong with that. But most MMORPGs implicitly discourage that, as there's nothing out there for you to find.
Astellia took a different approach, and made exploration into a major game mechanic. Collectively, it's called Star's Tale, and there are nine parts of it. Each region has a list of things to find, except that Lentuth is split into two region for Star's Tale purposes. In addition to achievements that grant you asper (the in-game currency), you get various rewards at each 10% threshold for completion of a zone, including a three star or higher astel at 50% and 100%.
You generally can look up the location of Star's Tale components if you want to. I recommend trying to find them on your own, and only looking them up if you give up. You can readily catch a lot of pieces so long as you're looking around as you play through the game. Star's Tale items are always in the open world and never in instanced dungeons, other than the dungeon completion part itself.
You don't actually have to do Star's Tale if you don't want to. All of the rewards from it except for those used to complete other portions of Star's Tale are obtainable by other means, such as farming dungeons. It's completely optional, and I suspect that most of the people who say that they briefly tried the game and hated it didn't even notice that Star's Tale is part of the game.
There are nine separate parts to Star's Tale, and I'll detail them here. First is the Maglev Adventure Journal. Each zone has four blue quests (that is, quests where the giver is marked by a blue question mark, rather than the usual green or orange), and those four quests count toward Star's Tale.
What makes the blue quests unusual is that they don't tell you where to go. The quest text might tell you what zone to check, but there's no quest marker to say exactly where to go. The quest giver himself might be hiding, and isn't marked on the map. Each quest has two to four steps after acquiring the quest, in which you have to find some particular item and click on it. For example, the first one, Kiyo Behind the Cave, asks you to find a basket of fish. The steps must be done in order.
The second part is Forgotten Story. There are various places that you'll find something laying on the ground, such as a scroll or book. If you click on it, you'll get a five minute "buff" that enables the next part, but doesn't affect your stats. Each region has eight such chains, and they generally have two to four parts each. The parts must be done in order, and the buff that you get from finding one component is required in order to be able to get the next component. The text sometimes gives you hints as to where to go.
The Forgotten Story parts can be hard, precisely because they have to be done in order, and with the five minute timer. You also lose the buff if you click on an item for a different line or one of the hidden boxes, or for approaching certain spots with storyline significance. If you look around, you'll likely find a lot of notable things laying around that look like they're some step of a Forgotten Story chain, but if they're not the first one, it can be a little tricky to figure out what they go to.
Third is Hidden Boxes. Most zones have two to five treasure chests scattered around the zone. Click on a treasure chest to get some ancient fragments, as well as completing an achievement that gives you some asper. Finding all of the hidden boxes within a zone gives you some zender from an achievement, and for all of the zones in a region, some more zender. You have to accept the achievement completion to have this show on Star's Tale.
The treasure chests for hidden boxes all look exactly the same. Some of them are just laying out in the open, while others are tucked behind something, such as a tree or a crate. If you see one, getting to it to click on it is never difficult. This isn't like Guild Wars 2's jumping puzzles. Even if you don't do most of the Star's Tale, I recommend picking up the hidden boxes that you happen to find.
The fourth component is ancient monsters. Most zones will have one particular monster marked with a title of "Ancient". It sometimes looks a little different from others in the area, but often not. Sometimes, it is tucked in a relatively out of the way place. Basically, you have to look around the zone to find it. Kill that monster to complete an achievement. Unlike hidden boxes, for ancient monsters, you get Star's Tale credit immediately, rather than only when you complete the achievement.
The fifth component is Viewpoints. These are somewhat analogous to vistas in Guild Wars 2, but they aren't marked on your map. Basically, you click on a viewpoint and get a short cut scene that shows you the area. Viewpoints look like a blue light or blue flame, and all look the same. If you can see a viewpoint, it will be easy to get to it.
The sixth component is Field Bosses. These are different from, and much weaker than, the field raid bosses that are scattered through the game world. Each region has two field bosses that are by far the strongest monsters in the region. Get a party, or else wait until you've leveled far past the boss, then come back to kill it. Killing the boss gives you Star's Tale credit.
Seventh is dungeon completion. Each region has two or three dungeons. Completing them at solo and party difficulties separately count for Star's Tale credit. Scenario and legendary difficulties do not count.