Kant is saying, as I read him, that if there is to be such a thing as knowledge of external objects, then there must be "self-consciousness"(memory, for example, that allows comparison) of the person experiencing them. He argues that the this person, or subject, experiences them according to certain common categories.
For consciousness, there is not a "that object" but just-that- particular- object- and-not- another; we do not immediately intuit an object, but given sense-stuff/data:
"Now all experience does indeed contain, in addition to the intuition of the senses through which something is given, a concept of an object as being thereby given, that is to say, as appearing." (A93/B126)

Kant maintains, then that to formulate an OBJECT, a this THING, it must be conditioned by both the Transcendental Aesthetic (space and time) as well as the Transcendental Analytic (the twelve Categories of the Understanding.

I have a bunch of sense-data intruding on my self; it is a rock (of such a shape and place, heavy, there is only one of them, it is now just in front of me, and so on). It is what it is not because of the raw sense-data, but because it is conditioned by a unified Self, and these conditions are the same for everybody.

This is a better explanation than mine:
Kant: Transcendental Deduction

Here is the bit I am going on about:

"It must be possible for 'I think' to accompany all my representations; for otherwise something would be represented in me which could not be thought at all, and that is equivalent to saying that the representation would be impossible, or at least would be nothing to me." (B132)

"This thoroughgoing identity of the apperception of a manifold which is given in intuition contains a synthesis of representations, and is possible only through the consciousness of this synthesis. For the empirical consciousness, which accompanies different representations, is in itself diverse and without relation to the identity of the subject. That relation comes about, not simply through my accompanying each representation with consciousness, but only in so far as I conjoin one representation with another, and am conscious of the synthesis of them. Only in so far as, therefore, as I can unite a manifold of given representations in one consciousness, is it possible for me to represent to myself the identity of consciousness in [i.e. throughout] these representations." (B133)

---------- Post added 07-15-2009 at 07:38 AM ----------

I think I need to work through Curtis Brown's rendition of Kant's argument a bit more to see where it corresponds to the text. Thanks for shedding light.