Binding is the process of establishing an association between a Rig and a Mesh for a given Pose. In Blender this association is established by creating an Armature Modifier. This Modifier is assigned to a Mesh and associated to an Armature.
In general the Bind Pose can be any user defined pose. However, Blender (currently) only supports binding to the Rest Pose.
Note: In Blender we often see the term Parent to Armature (deform) which is used as Synonym for Binding.  Actually this has a historic reason: In Blender’s first days binding was technically implemented by parenting the mesh to the Armature…
However, since a few years Blender binds the mesh to the armature by using an Armature Modifier. The menu entry for parenting to armature deform has been kept mostly for convenience and ease of use.