Effectors are a means to affect a target item, generally a mesh layer, to deform it in specific ways. The Rotation Effector, when assigned to an item, rotates the target item. This is the same as a regular item transform, but you can link this to rigging and control it through the Schematic view because it is an item with channels. With a regular tool, you can only control it when it is active.
You can add an Effector by using the Item List's Add Items command, but it won't produce the intended result because it only places the Effector in the Items list. For proper results, you must connect the Effector to the mesh layer by way of a General Influence. The General Influence acts upon the mesh, and the Effector itself, produces the instructions on how the Influence should modify its target.
If you add the Effector in Items mode, Modo connects the Effector and the mesh layer automatically. First, select the target item(s) either in the Items list or any 3D Viewport and then right-click the item and choose Add Deformer > Effectors > Choose Type. Also, you can select the target item(s) and click the Effector button in the Deformers sub-tab of the Layout interface. Once you create the Effector, you can position it and modify its values to produce the desired results. When you apply an Effector to multiple items, Modo deforms each affected item based on the Effector's relative position to the mesh.
Name: Displays the current item's name. You may change the name by clicking the current name and typing a new name.
Position XYZ: Indicates the numerical position of the Effector item in XYZ space. These values define the origin of influence for the Effector.
Rotation XYZ: Indicates the rotation of the Effector item numerically. Changes in these values from the rest position transform the deformed target that amount. (Modo determines the rest position by the item's position in the Setup action state.)
Order: Indicates the order that Modo applies rotations to the Effector item. By changing this order, you can sometimes reduce or eliminate gimbal lock.
Scale XYZ: Sets the size of the item's representation in the 3D Viewport numerically. (This does not transform the target item.)
Reset: Resets the selected transform values to (0,0,0) and returns the item to its default state.
Zero: Resets the selected transform property values to 0 but leaves the item's position and the mesh position intact. Modo does this by adding a negative transform item to the Mesh Item's channels.
Add: Adds a Transform item to control an item's position, rotation, or scale. By default, new items do not have any transform items associated with them (although they are visible within the Properties panel). Only add the necessary transforms on an as-needed basis to reduce scene overhead. You can also use this Add function to add a selected set of transforms to the Channel list while keeping the default 0,0,0 values, which is necessary for Referencing. (To override channels, they must exist.)