There are two parts to a tree.
One part is its physical existence: that which reflects light and creates a sensory impression on the brain, allowing it to be physically perceived. The green leaves, the branches, the trunk, the bark...these are its external traits.
But it has internal traits, too, and these are precisely what the words that I use to describe the tree represent. When I say those words, an image is conjured in your head, a vague generalization of what a tree looks like. But that is not a real "tree." That is intuition: the vague representation of that which innumerable physical entities are actual manifestations of.
In this sense, language is a manifestation of human intuition. It is symbolic. It takes physical creates (sounds and pictures) and uses our capacity for symbolic interpretation to attach meaning to them. A leaf is not actually a tangible thing; it is a term that is used to refer to a "type" of thing.
Now there is another kind of intuition, one which examines not names of things, places, or any other kind of proper kind of tangible existence, but the processes that these things can be observed as parts of. Take the verb, "run." It is not the act of running in any specific sense; it refers to the abstract process that all instances of "running" have in common: the movement of the legs such as to propel the physical body. "Running" refers to all instances of this particular kind of movement that take place.
This is intuition. This sense of "sharing" qualities, or "not sharing" them, is what is examined by intuition. Intuition takes tangible, physical qualities, and abstracts them so that what is being observed might be related to other instances of the same physical qualities
Example: many people relate Ni to nostalgia in some ways. Here's why: we often find ourselves in a place, or hearing music, or speaking with a person, or performing some activity, and it reminds us of something we have experienced in the past. This "reminding" is the association of qualities of the present moment with qualities of another place in time. This is the "connection," the line between the past and the present, that is drawn upon making an association. Say I find myself in an airplane, looking out the window. In this situation, I am simultaneously bombarded in my own mind by feelings of wist, of times that I have flown to college, back home, to visit grandparents, to go to their funerals, to see friends, to leave them...the awareness of the "similarness" brings me back to all of these circumstances that share the abstraction of "looking out of a plane window" and brings all relevant experiences to the surface.
Next installment: Intuition as an "internal" element.