I googled the vector field and I learnt that it's a kind of particle system. This should be correct because all PVFs are in the particles package. Whatever, it's beyond my knowledge.
Anyway, it's not a high priority task. There are only two PVFs in the game assets, and they even don't have regular names. Seems that even Taleworlds doesn't take it seriously.
Not exactly, a vector field is like a 3D area (field) where for each point, we can indicate a direction (vector). Usually this is represented using a 3D texture, where the rgb values represent a 3D vector (not necessarily normalized). You can think of it as a 3D flow map if you are familiar with that.
This is usually used for particles as you mentioned, to simulate wind or some kind of motion on particles on a small scale.
Now about the procedural part, I'm really not sure what they mean by this. It could be that the vector fields can be created on the fly and can change over time, so that they don't need to store a 3D texture for that, but instead it's represented by mathematical functions.
I didn't notice any example of them being used in the game so far (maybe on the title screen?), so yeah, probably not the highest prio for now.