Summary
Experience points are used to level up your character.
You get experience from killing mobs and doing quests.
Experience From Killing Mobs Guide by ShadowFrost
Contributors: Drycona, Bardou, Syreen, Naiya, and Relict
Link to guide: Experience Guide by ShadowFrost [Official Forums]
This guide can be used to find the optimal place for a party to grind. The table should be simple enough.
The first column is the monster's level in relation to you.
The second column is the percentage of base experience you would get from it.
Exp continues to diminish as the level difference widens. More numbers to be updated.

Example: You are level 15. The monster is level 20.
You would use the "+5" modifier, which is 115%.
What this means: if the monster would give 500 exp for killing it, you would get 500 *1.15 = 575 experience from the monster.
How to best use this knowledge:
The best way to optimize experience for your party is to find an area where the mobs give at least 100% exp to every party member (if possible).
Additionally, attempt to find an area about 8 levels higher than the lowest member of your party. If both of these conditions are met, the party will
benefit best as a whole. For example: you have a level 60, 65, 70, and 75 in your party. To meet the first condition, you would have to attack
monsters near the level 69 range. This way, the level 75 and 70 both get 100% exp. It just so happens that this also allows the level 60 to gain
a 30% bonus to exp and the level 65 a 10% bonus.
Obviously there are other situations in which you cannot give everyone the best exp possible, and the more varied the level of the party members, the
more difficult it will be to find an ideal grinding area. If you have any questions, please feel free to post here or PM them to me directly.
Experience Boost Stacking
All experience boosts, excepting premium boosts stack by multiplying with each other.
Premium boosts, on the other hand, add with each other, and then multiply with the other experience boosts.
Here's an example to illustrate what I mean:
Suppose your nation possesses 1 castle (3%).
You also have beast lore (5%).
You are fighting something 8 levels higher than you (30%).
You have a gold premium account (Premium Boost: 45%).
You are using an experience badge (Premium Boost: 30%).
Your total boost to exp would be calculated thus: 1.03 * 1.05 * 1.3 * (1 + 0.45 + 0.3) = 2.4604125.
That is to say, that under these conditions, you would be getting almost 2 and a half times as much experience as normal.
Additionally, experience is truncated, not rounded. What this means: in the scenario above, where you get (2.46 x BaseEXP), if
we assume that you would get 123,456 exp normally and you apply the bonus, you get 123,456 * 2.4604 = 303,752.6856.
If we were working with a rounding system, that would round to 303,753. However, EXP truncates, so you lose the bonus 0.68 exp
and end up with 303,752. This is probably not all that important: just technical stuff.
EXP to next level (tnl)

Sources
Some EXP tnl taken from Info Gathering [Official Forums]