Intention is Intent-Ion. A charged entity with an objective. In physical terms an atom has negative and positive charges and when it loses one of these, the other takes over and the atom is now an ion and consequently exerts a force which is biased towards similar or opposite type of charges. In other words intention is a biased energy that directs action in a certain direction.
In contrast when we say muso no kamae, and refer to a no-intention attitude, the first picture that comes to mind might be the absence of everything, but in the context of the physical analogy above you would be an energized being but with no bias in any direction, i.e., you are completely neutral to any objective or goal. This does not imply that you do not move towards any objective or goal but only that you are equally likely at any point in time to move towards any objective. A state of complete freedom not bound by directional goals.
Interestingly when you search muso on the internet one of the results that come up lists the meaning as “The Only One”, or “Without Equal”. This can be interpreted as being in the centre of everything, “naka ima” and therefore being the only one truly real. It can also be taken as a duality of being both an immovable object, fudoshin, and an irresistible force(Fukakōryoku?) which would then make an entity “without equal”. In all cases it is a state of energy and potential to drive action.
Applying this view of intention to our perception of muso no kamae, we can visualize an infinite number of forces pushing outwards in all directions equally and thus balancing each other out. But what they also do is expand our universe (utsuwa) through their outward force. They can then translate to actions (tamashi) anything that falls in this space. The potential to influence the universe through the actions is then the sainou that is in all.