The 2 bone solver is ideal for posing joint chains (such as arms and legs) that you want to stay in the same plane. For example, the shoulder, elbow, and wrist joints of an arm driven by a rotate plane IK handle all stay within the same plane as the elbow rotates. The plane itself can be rotated from the shoulder joint by the pole vector.
The 2 bone IK solver is a subset of the rotate plane IK solver. Therefore, IK handles with the 2 bone IK solver solve the rotations of their joint chains in the same manner as a rotate plane IK handle. See Rotate Plane IK solver and Rotate Plane IK handle components.
The two bone IK handle is meant for posing and animating short joint chains that consist of three joints (two bones). If you try to pose and animate a longer joint chain with the two bone IK handle, then the 2 bone solver will solve for the rotations of only the start and second to last joints and will ignore all other joints in the joint chain.
The 2 bone solver is the fastest IK solver in Maya. This makes two bone IK handles ideal for setting up characters in a game development environment. Maya includes the source code for the 2 bone IK solver plug-in so that game developers can replicate the exact behavior of this feature in a games engine or modify the code to create their own custom IK solvers.
The source code for the two bone IK solver is available in the devkit\ik2Bsolver folder of your Developer Kit installation. The source code provides an example of how you can create your own IK solver plug-in. Also, by extracting the core algorithm, you can replicate the exact behavior of the 2 bone IK solver in a games engine. For more information, please read the README file in the ik2Bsolver directory.
The Developer Kit is available on the Autodesk Developer Network.