Gothic works are often cited as looking like a deck of cards placed one behind the other.
The advancement over this was to leave the deck of cards but space them out a bit so as to have perspective. The final element to be added (interlock) was explicitly given in the present example.
In this step, the artist joins the cards in the back to the cards in the front - not just layering them, but integrating a third dimension as a clear logical necessity. This is the difference between Adobe layering programs and a 3D art/cad suite - the front card is the continuation of a rear card with something standing between and cutting off any continuous view.
You can't do this easily. It takes time to make it look right. This sort of thing cannot be mass produced in an attic in Mexico for the "starving artists" sale at your local Ramada Inn. Modern painters will not do this - only those who are a "cut above".
I am absolutely certain that Rubens placed this branch just to state the principle in a obvious way (not for the aesthetic reason of "interest" given next page).
Philosophical InterlockAs is often the case, there is an analog in the philosophical content of an artwork.
An example is Raphael's School of Athens in the Vatican. In this work there are several groupings of figures engaged in philosophical discourses. Aristotle and Plato walk "parapatetically" center stage.
The groupings are arranged in a fashion analogous to perspective, i.e. they support the central figures by being lesser points of interest but not directly. They are not interlocked with the central group.
If there were two figures on either side of Aristotle & Plato ... with a rope in hand, ready to bring it taught and thus trip the dynamic duo (as a joke ; ) ... then, these figures would be interlocked as well as subordinately supportive of center stage.
There are many figures in art works which are both physically and philosophically interlocked (as in a battle scene), as well as detached figures interlocked with others only philosophically (as in a religious crucifixion painting).
I hope this example makes clear what I mean by philosophical interlock. It is realized only by master artists.