Now, at first I will take a look at those things here listed and do some maths with quaternions.
1) Bind Pose
2) Inverse Bind Pose
3) Bone Hierarchy
4) Animation in Local Bone Space
5) Interpolation of local space bone transforms to play back animation
6) Create the pose for the skeleton at the current frame from the local space transforms by transforming by parents
7) Transform the absolute transforms by the inverse bind pose to combine those transformations
8) Send vertex & matrix data to the GPU
9) On the GPU: Calculate the position of the transformed vertex by the bones it's bone indices point to, ......
Probably there will be some more questions later