I don't know where that quote originates from, but in reference to intention, it sort of works like this...
Firstly, intention is a potential in the mind which doesn't fully engage until it is expressed through one or all of three mediums, in those cases intention then becomes kamma, which simply means action from which something is put together in the world. Those three mediums are voice, physical actions and thoughts and are sometimes referred to as sankharas often translated as intentions, which may or may not be helpful. It becomes problematic when fragmenting this into a process, due to determining where the intention lies. The punchline is that it lies nowhere, that is the illusion. At best, one could say that intentions are self-ideas that lose themselves to gross feelings, but we have to speak about it as though it is 'something' to look for, so that one can see it is not actually there.
That potential (intention) is made up of a few things: firstly, something has to colour or impede a sense organ. Let's say someone walked into your room and this person caused you some upset several weeks ago. Your eye points towards that person, and in that instant of connection, there is a subtle sensation. Baked inside that sensation is an interpretation or a perception, but it is not intelligible to the conscious mind, therefore it bypasses the objective reasoning attributes of the mind and kickstarts those familiar gross feelings like irritation. In this particular scenario, the sensation has an aversive quality to it, which fires up irritation. This may then lead you to perform an action: perhaps you'll shout at them (speech); perhaps you'll stick your middle finger up at them (actions); or perhaps you'll think nasty things about them (thoughts).
This largely unseen sensation/perception boots up a gross feeling like irritation or anger. It is inside those feelings where a person seems to emerge, simply because we didn't look closely at what was happening in the body. For most people, these subtle sensations/perceptions are lingering just on the periphery of their awareness, so one meanders through life responding unconsciously to these subtle sensations, and wonders why they suffer so much.
The fascinating thing about this is, when one tries to find who owns those sensations and their resulting actions, there is nobody there. I remember when that collapsed for me. I was looking into this person who thought he was angry; I persistently looked in and around the anger, and one day, the illusion broke apart. There was no such thing as intention. That was fetters 4 & 5. Those two fetters create such incredible kamma, it's actually quite astonishing! They are the rebirthing fetters. In the Theravada scheme, having broken those two, one is then seen as a non-returner, as no more rebirthing kamma can be created, so severing fetters 4 & 5 stops a lot of suffering.
The idea that there is somebody there is the illusion, and how do we define an illusion? Something that initially appears to be there, but which isn't. That is why the Buddha said, "form is like a glob of foam, feeling a bubble, perception a mirage, intention a banana tree [hollow and empty,] consciousness a magic trick.