PvE stands for "Player versus Environment". It represents you, the player, versus the surrounding world. Mobs, bosses, dungeons - that's all included in PvE. PvE is done in a series of a single base turn.
Monster's turn. The monster will always hit first and the mob will always hit second. Hitting them is dependant on your accuracy vs. their dodge, and vice versa for them. This is called hit chance. If they hit but do no damage, it's considered a complete "block". When you hit, you subtract their defense from your attack power. That's the damage, and it's then subtracted from the opponent's HP. If your speed is higher than theirs by a certain amount, you will have a second, quick attack. Same for them. When either mob or monster's HP is 0, they're KO'd. Opponents are computer-controlled.
Mob's turn. Your monster has a stat called "block", which is derived from (constitution * 1.5). This can be thought of as "fluff HP" - it regenerates every battle and is expendable. The bloak soaks up the damage so it doesn't hit the HP. Once the block is gone, however, the HP will go down and obviously when it hits 0, boom... dead. Mobs also have an ability that will happen with a 20% chance of each round.
Finally, if you have a lot more speed than the mob, you can get another attack in on them, for 60% direct damage of your speed. When you've won a battle, your fury meter goes up by 10%. When it hits 100%, you can spend it to make one giant, strong move for 0 energy.
There are 3 styles of attack. Fierce, normal and cautious. Fierce gives a boost to your attack, but your defenses go down. If you miss in fierce style, your monster might trip and take some damage. Normal is the standard attack and is the most popular choice among breeders. Cautious gives you more accuracy and defense while sacrificing a little bit of attack and speed.
PvE - Status Effects
Status effects are things that deal damage to your monster, or to the mob you are facing, because of different scenario's. For example, let's say your monster has a "barbed" equip. This means it has a chance to cause bleeding on the mob every round. While mobs attacking you can only do a status effect for so long, your status effects to the mobs last until either party is dead. The status effects are as follows:
Burned - Takes +10% damage from attacks.
Poisoned - Takes damage equal to 10% of maximum life every round.
Bleeding - Takes damage equal to 5% of maximum life every round, and attacks hurt 5% less.
PvE - Mob Sets?!
There is a type of "random" factor when you face a mob. It's only more realistic that every mob you fight would not have the exact same stats, right? Well they don't! There are five "sets":
Just because you're facing a mob whose set is "very easy" doesn't mean it particularly is an easy mob; it's a relative term. Normal implies that the mob is "supposed" to be this way, that's their average. If you'd like an example of how this set thing works, I will give you a short scenario.
You're facing a vicious rabbit, rawr! He comes out, he's got 20 HP, and you end up beating it. You beat a very easy version of the rabbit. However, his friend hears about it, and he's out to get you. (no, this does not imply there's a vengeance system) He's ranked a very hard mob, and he ends up beating the crap out of your monster. You'll notice the HP of the mobs will be higher or lower than some other of the same species... this is the best way to tell just what set that mob is in!