Today, there was a discussion among some of the North American disciples on intent. What is it? What does it mean?

The discussion allowed me to solidfy a couple of things.
In 2019 Iowa Camp, shifu mentioned:

Spencer's notes:
The camp’s lessons this time were pervaded by the idea of “intention”. Intention in PM is what we call “to lead”. For example, in the positive circle, the elbow in is the “lead” Intention has no meaning in itself, but it changes everything. I am starting to realize this is one of the reasons Master Chen’s form looks so much different than mine and I can never figure out why. Your eyes can only see movement. The act of leading translates to intention, and when intention is used, the action is different. In with elbow, turn at waist, out with hand… You have to be clear about those intentions. Say them aloud! When the intention is clear, you produce a very thin line. From one large thing, you pull out one dot. This is the concept of silk reeling.
My notes:
Lead - Intention
Intention can only be seen if there is movement, or change in structure.
When the intention is different, the result is different.

In with elbow, turn with waist, out with hand.
We need to say it out loud.
They make a triangle.
Isolate the three lines.
The triangle becomes a circle because of the rotation of the centre (which is an illusion)
3 independent ways to lead
3 intentions

Hugo mentioned water drop rolling down the window.

Shifu also mentioned before, "Real intent is no intent".

My thinking at the moment is that it is about the inevitable consequence when something is done. Nothing needs to be forced by me.

If A is done, B must become the result, then A is an intent. However, there is a relationship between A and B that must be maintained, otherwise, A is not an intent. e.g. A is your push on a revolving door, B is the resolving door rotating and hitting you back. The relationship is that the solid door with a non-moving axis that it can rotate on. With that relationship, you know that when you do A, B must become the result (there is no other possibility). A is indirect with B.

The word "lead" means going first, e.g. every section of a bicycle chain must go through the same spot one after another. The first one going through is the leader. This is also related to the concept that our actions must be vertical (going in the direction of the length of an object) and not horizontal.