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Zeliard:

The Story
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About the Game
Friends
Items
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Enemies
Boss
Walkthrough
Maps
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Game Internals
Fun with Bugs
Story's End
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Game Internals

Several gamers have noted different behaviours in the game which would give clues to how the game is keeping track of progress internally. Also some hackers, particularly Crystal, have been able to poke into the code for the game itself and have been able to confirm several findings, as well as present many new ones. I've tried to list out all the ones that I am aware of below.
In the following discussions 'level' refers to your power. When you start the game, you are at level 0. Every time the Sage increases your power, you level-up

Sword Damage

Gamer Adam Goode notes that swords become more powerful the more experience you gain:

The Training Sword is NOT the most useless sword in the game. I used my training sword right up to the Caverns of Corroer/Cementar, and I was doing just as much or possibly more damage than I would have been with the Spirit Sword. For some reason, after defeating a boss (or maybe it was the next level up by the sage... it was usually around the time I would travel to the next cave), the damage potential on the sword would increase by 1 point. When I got to the 2nd level, my training sword was doing as much damage as the Wise Man's Sword. By the 3rd level, it was in-between the Wise Man and the Spirit Sword, and by the 4th level, it was on par with the Spirit Sword. I only upgraded to the Knight's Sword in order to combat with Vista. However, this leaves the potential for never having to spend any money on a weapon through the game if you can manage to beat the 6th and 7th levels with only the Knight Sword.
Mokona makes the same point:
And what I found out just recently - it seems that the more you "level up" the more damage you do with any sword. I'm still not sure of it, but since I leveled - I began killing a certain monster with one slash instead of two. Sword was the same.

I have to add that I have personally experienced this effect too, but I was never really sure how it worked. Hacker Crystal sheds some light on the subject with her intensive findings:

The swords have a base damage of:
Training Sword1 + level / 2
Wise Man's Sword2 + level / 2
Spirit Sword4 + level / 2
Knight's Sword8 + level / 2
Illumination Sword16 + level / 2
Enchantment Sword255 + level / 2

If your level is odd, it rounds down, so three level gains is the same as two, for damage. You only go up in damage power every second level up. (Levels start from zero.)

So a level 4 character with a Training Sword has the same attack power as a level 2 character with a Wise Man's Sword. A level 255 character with the Training Sword will (barely) do half the damage of a level 0 character with the Enchantment Sword.

So, the moral of the story is, Mokona [and Adam Goode were] quite correct that damage goes up with level! Another good reason to fill out your life meter before fighting the Dragon! (And, in fact, leveling up even after your life meter is full will increase your sword's damage, of course.)

Experience Points

Hacker Crystal was able to find lots of information about how Experience points are calculated by the game. When you reach a certain number of Experience points, then the Sage can increase your power - that is, you level up. I'll let Crystal explain in detail:

The game keeps track of your level and experience internally; you start at level 0, with 80 health (2 of 20 bars)
Each pixel is 8 health, so when the bar is full, you have 800 health
This happens after fifteen level ups. For completeness' sake, the health values at levels zero through fifteen are:
LevelHealth Points
080
1120
2160
3240
4280
5320
6380
7460
8540
9600
10640
11680
12720
13760
14780
15800

Note that it doesn't just go up by the same amount every level!

The experience required for levels one through sixteen are as follows:
Experience Required for Leveling Up
Beyond that, every level costs 60,000. The highest possible level is 255. If you reach that level, not even Sage Indihar can help you improve anymore.

Note that the above experience numbers are per level, not the total you'll have gotten by that point! So by level sixteen, you'll have gotten a minimum of 220,420 experience (i.e. the sum of all experience points required to level up from level 0 to 16). This is because when you level up, it subtracts the amount above from your current experience.

So if you're level zero (haven't leveled up at all), you'll need 50 experience to level up. However, if you have 80 experience, only 50 is needed to level up. So after you level up, you'll have 30 experience left over.

There's a catch, though! It won't let you hold onto enough experience to level up again without killing anything. For example, lets say you're at level 0 and you have collected 400 experience. To level up you only need 50 experience and the next level after that is 150 experience. So if you leveled up, you'd expect to have 350 experience left, which is well beyond the 150 you'd need to level up again! But instead, it reduces it to 1 less than you need, so you end up with only 149, instead of 350. So beware of wasting experience!

You gain experience by killing monsters. The Enemies and Boss sections have information about how many experience points you get by killing each type of enemey.
The most experience you can hold at one time is 65,535. So, that is another way to waste experience, especially in the late levels where all the monsters give you a large number of experience points!

Also, "You must persevere" means you're not 50% of the way there yet; "You must accumulate more experience" means at least 50%, but not 75% of the way there; and "I see the faint light of the spirits" means you're 75% of the way there.

Some interesting things to note are that Alguien gives 30,000 experience, while Jashiin only gives 10,000. Since all levels from 16 on require 60,000 experience, that means you can simply fight Alguien twice, and teleport back after each, rather than fighting all the way through!
So two Alguiens for each level after 16. Or, 236 monsters (all of the monsters in that last cavern give 255 experience each). Or, one Alguien, one Jashiin, and 79 monsters.

Gamer Gowtham Kumar mentions a faster way to gain experience points. I have not tried this out personally, so am not sure how well it works:

A comment on the experience amounts calculated by our dear friend [Crystal]:
If you are in the lower levels(eg. Muralla/Satono/Bosque) the fastest way to power up is to kill yourself. That will give you more experience.
Especially, in level 1, I kill myself once, get powerup from sage, then kill myself twice, get powerup...

This can be done with speed 9 (press F9, speed 9)
Thus power-ups till the life meter reads half maximum can be made really fast this way.

Shield Strength

Gamer Adam Goode also notes that the Light Shield, although having the same numerical strength as the Honor Shield, can take on much more damage before breaking:

The Titanium and Light Shield are in a class of their own, above everything from Honor Shield and down. For a good example involving the first chance to buy the shield, go outside into the caves. The nearest creature will typically do about 5 damage per hit to your shield. Equip the Light Shield and go outside. Suddenly, they are only doing 2 damage per hit. Therefore, the Light Shield is a useful upgrade to help your survive the 6th level and Tarso (albeit not a long one, since it would be smart to upgrade to Titanium Shield as soon as possible).

Anything Else?

If you're familiar with more 'inside secrets', let me know and I'll put them up on this page too.