Figure1: A 3D model in T-pose and bones placed in it
Modellers model the characters in T-Pose so the riggers can rig the character more easily. This helps them to place the bones and adjust vertex weights and envelopes easier. When all the bones are placed in the 3D model and the skinning process starts, the current pose of the skeleton is saved. This pose is called Binding Pose. The name shows the whole story. Binding pose is the pose where you start binding a mesh to its corresponding skeleton.
Now why a binding pose should be saved ? You might know that all of the vertices positions initially should be calculated in modelling space. A skinned mesh's vertices are transformed by it's corresponding skeleton. When the skeleton bones transform, the vertices' positions change based on the weights they have for each bone (bones transformations are calculated in mesh's modelling space (object space)). Now if the vertices' positions change based on the orientation of the bones the whole mesh will be distorted because of an extra orientation or maybe position that the riggers applied to bones to adjust them into meshes. The rigger transforms each bone to fit them in the mesh's body. These transformations (call it Binding Pose Transformation) should not be calculated for the final vertices positions. You can consider an example in which you have a skinned mesh, so by changing bone transformations the vertices positions should be changed as well. Lets consider just one bone rotation. The orientation of the bone in mesh's modelling space is equal to:
Bone Orientation = Binding Pose Rotation * KeyFrame Rotation
If vertices get affected by the "Bone Orientation" variable, first they will be rotated by Binding Pose Rotation and next with the key frame rotation and that binding pose rotation will distort all of the vertices because the initial model that the modeller created is affected by some extra unnecessary rotations produced by the rigger. So for bones belonging to a skeleton of a skinned mesh, a reference pose have to be saved and this reference pose is called Binding Pose. It will be saved when you apply a skin modifier to your mesh or in other words when you start the skinning process. For each bone in character animation, all of the key frames are stored relative to its binding pose. Now for a skinned mesh, deformations occur based on the relative transformations of each bone to its binding pose. This will prevent the mesh to be distorted.
For animation blending each bone has a weight. The weight is ranged between 0 and 1 which 1 means the full calculation of the key frame transformation and 0 means the binding pose. Now any other number between 0 and 1 for a weight shows a blended transformation between bones binding poses and key frames transformations.