How everything is connected, or: why your edited mesh moves weirdly
This page will give you a short explanation on why 3d objects are moving.
To learn what a rig even is, check Armatures: .rig files
Maybe you want the Weight Painting for Gonks guide?
For a documentation of the import/export options in Wolvenkit, check here.
Guides on how to transfer weights between rigs: blender plugin, youtube video, wiki page
The connection between a mesh and a rig is made via vertex groups. Any number of vertices can be assigned to a group, which is then matched to a rig's bone via name.
How much every bone influences the vertices is determined by vertex weight, which can be altered in Blender's Weight Paint perspective:
Vertex weights are assigned for every vertex group, and each vertex will move on the basis of the sum of all its weights.
To preview the deform in Blender, you can select the mesh's parent armature and enter the "Pose Mode". There, you can either apply an exported animation, or select individual bones and rotate/move them. The Armature modifier will morph your mesh according to the pose, letting you spot errors much faster than trying to debug them in-game.
You can see a video of the process here (courtesy of Vesna).