What are the vertex influences?
When you have bones assigned then vertex influence is how much the vertex is modified when the bone moves. Its the bone-weight pair.
yep. As i understand it the when your using an armature/bone vertex points are assigned to the bone. When the bone moves all the vertex points associated with the bone move too. You could say the amount the bone influences its vertex points is 100%. Half-life models work like this. The problem with this is that bending doesnt look realistic and the model deforms strange under extreme bending. However other model formats try to imporve on this by allowing the vertex points to be owned by multiple bones/joints. Instead of a bone having 100% influence on a vertex point the bone may only influence the matrix(positional/rotational info)of the vertex point by say 40% while another bone influences the matrix by 60%. This allows for better deformation of the mesh. These are refered to as bone-weights. So a vertex point would have multiple bone-weights, usally scaled from 0 - 1, that when multiplied times the maxtrix of the vertex point will give a new pos/rot matrix for the vertice.