A transform controller is a controller that controls a Matrix3. Transform controllers control the 4x3 matrices used to define the position of nodes in the scene for example. The first reference of a node (i.e. accessed via INode::GetReference(0)) is to it's transform controller.
This controller governs the position, rotation and scaling of the node in the scene. Developers can conveniently get and set the transform controller used by the node using INode::GetTMController() and INode::SetTMController().
Most nodes use the PRS transform controller (for example mesh objects). Other items (such as target spotlights and cameras) use the Look-At transform controller.
The default transform controller used by an object can be set by the 3ds Max user.