PvE means Player vs Environment (things in the game).

These PvE Elements include  Monsters, Resource(gathering) Nodes, and Furies. 

Each type of PvE element should appear on a specific land type (biome) with specific types of researching unlocking the ability to gather certain Resources or hit certain Monsters! 

Each type of PvE element also has a level. As you progress through your research you'll earn the ability to hit or gather from higher levels! 

Please keep an eye out for Special Abilities for your various Heroes as some of them are more attuned to certain biomes, and will have bonuses to your Might or Gathering Speed!