Different Pokemon Generations correspond to different games. For example Pokemon Red, Blue and Yellow are Generation I. PokeMMO uses ([i]mostly[/i]) [b]Gen III[/b] mechanics. For example, this is very important concerning moves as the type (electric, steel, fighting, etc) determines if it depends on either the Attack (physical) or the Special Attack (special) stats. Keep in mind that all Eeveelution type moves and dragon are special (Spatk based) while the rest are physical (attack based) in PokeMMO. A move split occurred after Gen III where the individual move determined it's own category (special/physical).
Generations also aid in determining the types of Pokemon you can catch, obtain, etc, the different moves your Pokemon can learn, how certain items function etc. Again PokeMMO makes use [i]mostly[/i] of Gen III in regards to item mechanics.
I hope this brief explanation helped a bit. Feel free to PM me on here, or in game with any other questions you may have, or if you need more of an explanation regarding this subject.