Shape authoring provides you with different tools to accomplish your shape deformation tasks.
Blend shape deformers let you change the shape of an object into the shapes of target shapes, such as for creating facial animation on a character. You can also use blend shapes to correct deformations on a skinned character's body, for example. You can use the Shape Editor to create and control all the blend shape deformers for an object, as well as create target shapes, set their weights and key them, create in-between shapes, create combination shapes, and so on.
See Blend shape workflows for information on different ways of working with blend shapes, and Target shapes, base shapes, and blend shapes for basic information that will help you understand working with blend shapes.
You use blend shapes with the pose interpolation system to create pose space deformations. This lets you add corrective or enhancement shapes to skinned and rigged characters based on a certain pose, and have those shapes interpolate as the poses move from one to another. You can use the Pose Editor to create pose interpolators plus their poses and blend shapes, and then control them, including altering how the shapes are interpolated.
See the topics in Pose space deformations (PSD), especially Create pose space deformations to get started.