This expression limits the possible position, rotation, and scaling of an object. Each axis can be handled separately. It is possible, e.g., to limit an object to movements along the x axis, or to allow rotations only around the z axis between -90 and +90 degrees. This works both for animations and editing.
The attribute manager seems to show quite a lot of parameters, but there are in fact only four different ones which are repeated for each possible transformation (rotation, translation and scaling) and each axis (X/H, Y/P, Z/B).
First you select (for the desired transformation and axis) the type of limit from the dropdown field "Limit".
You can set the necessary values in the fields "Min" and "Max". If you select the limit type Fix, the value in the "Min" field is used as fixed value. The GUI reacts to your limit type selection and allows input only in the relevant fields.
Moreover, the mode can be set to "Local" or "Global". If you use "Global", the limit works in the global coordinate system, no matter what hierarchy the object is in. If you use "Local", the limit works in the local coordinate system (the system - or coordinate space - of the parent object). You can check the repercussions of both settings quickly enough through the coordinate manager of C4D.
If you test the limitation on a real model, you will quickly notice a strange behaviour when using the three axis handle symbols in the view window. With freshly generated objects, everything works fine. You drag the x axis handle and hit the x axis limit somewhere, you turn the b axis handle and are stopped by the b axis limit. But as soon as you have turned the object, nothing works any more. You drag the x axis handle, and the object doesn't move at all, or not as it was supposed to, or it may even slide sideways although that should not be possible when dragging the axis handles! What happened to the poor model?
The seemingly strange behaviour has a simple reason. Limitations work in the coordinate system of the parent object (or even in global space). The handles at the axis cross of the object, however, symbolize the object's own coordinate system! And that own coordinate system may be positioned slanted at odd angles within the space that is actually limited by the tag. That means: When you drag the object around by its axis handles, you really move the object along more than one axis of the parent coordinate system.
You don't believe me? Try it: generate an object, turn it by 45 degrees, and drag it along by its axis handles in different directions. You can see in the coordinate manager that several axis values change at the same time, depending on the direction.
The tag "Limit Transformation" does not use the object's own coordinate system to calculate the limits (that would not make sense at all, because in respect to its own coordinate system, the axis values of an object are always zero!), but the parent system or the global system. The following image shows a visualization of that situation: The large cube, shown only by its edges, symbolizes the transformation limits (translation is limited to a certain range in all three axes). The small cube is the limited object. It is turned in two axes, but the valid limits are defined by the large cube that has not been turned!
If you drag e.g. the y axis handle now, the small cube will at first move unhindered diagonally through the limited space. Somewhere, however, it will hit the limit (the wall of the large cube). If you now continue to drag the small cube, it will not be able to continue into this direction: it will "slide along the wall of the large cube" until it hits the next wall. As soon as the small cube has reached all its limits regarding the vector of the drag, it will come to a standstill. In fact, the small cube will behave exactly like a real object in a limited space when you apply a directional force to it. If you now forget about the position and angle of the outer cube, the actual movement of the dragged small cube seems strange. Even worse appears its behaviour when rotated (although it really is the same effect at work).
If the coordinate system of the object lies parallel to the coordinate system of the parent object (or the global coordinate system), the dragging of the axis handles works intuitively again.
(Take note: The image is a bit simplified. The limits work on the zero point of the small cube, that is the base of its coordinate system. Only this point is kept within the limited area; points and polygons of the cube can naturally jut out from the large cube. The "Limit Transformation" tag is not a collision detection!
And one final detail must be heeded: "Scaling" refers only to the matrix transformation, the sort of scaling that is done by the object tool (not the model tool). The model tool does not scale the transformation matrix, but changes the parametric values and polygon points of the object. Such a scaling cannot be limited by the tag.