In the Biographia Litteraria, Coleridge split the mind into two parts, which he called the Imagination and the Fancy. He then subdivided the imagination. As he writes:

The IMAGINATION then, I consider either as primary, or secondary. The primary IMAGINATION I hold to be the living Power and prime Agent of all human Perception, and as a repetition in the finite mind of the eternal act of creation in the infinite I AM. The secondary Imagination I consider as an echo of the former, co-existing with the conscious will, yet still as identical with the primary in the kind of its agency, and differing only in degree, and in the mode of operation. It dissolves, diffuses, dissipates, in order to recreate; or where this process is rendered impossible, yet still at all events it struggles to idealise and unify. It is essentially vital, even as all objects (as objects) are essentially fixed and dead.

FANCY, on the contrary, has no other counters to play with, but fixities and definites. The Fancy is indeed no other than a mode of Memory emancipated from the order of time and space; while it is blended with, and modified by that empirical phenomenon of the will, which we express by the word CHOICE. But equally with the ordinary memory the Fancy must receive all its materials ready made from the law of association.

To put this into understandable English, imagination in general is the way we find the "hidden meanings" in the world. It is our creative force. The primary imagination is the largely unconscious way we watch and assimilate information and ideas from nature and the world around us. We make connections between what we see and our own lives and between different things that we see. It is the imagination that all people have. It is imitating God's creative process.

The secondary imagination, however, puts what it sees in nature together in new and different ways. It is original; it leaps to a higher level; it is the imagination possessed by artistic geniuses.

Fancy, to Coleridge (and this is very different, say, from how Worsdworth understood the term) was merely mechanical memory. It's recording "just the facts."

In "Kubla Khan," we primarily witness the primary and secondary imagination at work. Since this is a dream vision, the primary imagination provided the raw material that Coleridge's artistic brain reworked into a work of art.

The first part of the poem appears to come from the primary imagination: it is a recreation or imagining of a scene we might see in the world:

In Xanadu did Kubla Khan

A stately pleasure-dome decree:

Where Alph, the sacred river, ran

Through caverns measureless to man

Down to a sunless sea.

So twice five miles of fertile ground

With walls and towers were girdled round;

And there were gardens bright with sinuous rills,

Where blossomed many an incense-bearing tree;

And here were forests ancient as the hills,

Enfolding sunny spots of greenery.