This dialog can be used to change the anchor point of an object. The anchor point is a point inside the object that is used as the origin for all object transformations (scale, rotate) and also the position of an object is always relative to the anchor point. Sometimes the anchor point is also referred to as the 'hot spot' of an object.
The anchor point can be any point inside the object ranging from 0.0/0.0 (top left corner of the object) to 1.0/1.0 (bottom right corner of the object). The center of the object would be defined by an anchor point of 0.5/0.5 which is also the default.
For example, if you want to have an object that shall be rotated around its center point, then you need to set this object's anchor point to 0.5/ 0.5. If it shall be rotated around its top left corner, you have to use 0.0/0.0 as the anchor point. To rotate around the object's bottom right corner, use 1.0/1.0 as the anchor point. The usual setting is to rotate around the center, so you should normally set the anchor point to 0.5/0.5.
When using an anchor point different than 0.0/0.0, keep in mind that all position specifications will be relative to the anchor point now. This means that a position of 0:0 does not necessarily mean that the object will appear at the top-left display corner. For example, if you have an object with an anchor point of 1.0/1.0, moving this object to position 0:0 (top left corner of display) would make the object pretty much invisible because its anchor point is set to the bottom-right corner of the object. Thus, if you move an object with a bottom-right anchor point to position 0:0, it means that the bottom-right corner of the object will actually appear at 0:0. This obviously means that only a single pixel of the object will be visible. The rest will be off-screen.