"Intentionality is the power of minds to be about, to represent, or to stand for, things, properties and states of affairs." (Stanford Encyclopedia of Philosophy)
To talk about conscious states of mind being 'intentional' is normally taken to mean they are directed at something other than themselves, often things in the 'real world', e.g. to be conscious of the curtain in my room requires a relation between the curtain and my thoughts about it. But intentionality also implies a relation between me and my thoughts about the curtain (to the extent that 'I' and my thoughts can be dissociated). Moreover, there is an implicit relation between my act of thinking and the mental representation of the curtain about which I am thinking (on the grounds that the curtain, in this case, I think about is not a 'real' curtain in the world but a mental representation of it). So, we have at least the following terms in play:
1. ME –> 2. MY THOUGHT –> 3. OBJECT OF THOUGHT –> 4. OBJECT IN THE WORLD
What happens with this sequence when I think about myself? Is term 4 identical with term 1, i.e. am I as an object in the world the same as 'me' the person thinking about myself? Am I, as an object in the world, the same as my thoughts about myself, including my thoughts about objects in the world? And what happens when I introspect on my thoughts about my thoughts, i.e. when I contemplate my experience of my consciousness of something like the curtain, or myself? Surely my thoughts become in themselves intentional objects, multiplying the complexity of the 4-term relationship above.
It may be possible to disentangle this knot of relations, but it may be more fruitful to question the validity of the distinctions upon which the relations rest. Can 'I' really be dissociated from my thoughts, and can my mental representation of the curtain really be different from the curtain 'in itself', i.e. in the 'real world'?
One way to answer in each and all such cases would be 'yes and no'. Yes, we can draw a distinction between, for example, me and my thoughts about something, but at the same time we must recognise these terms are referring to something continuous, i.e. I am my thoughts about something. So 'no', the dissociation is not absolute.
The necessity for drawing distinctions is grounded in our primordial capacity to impose divisions on the continuous fabric of reality, the reinforcement of those divisions with language, and the consequent seeming 'naturalness' of the divisions in our everyday discourse. We are then put in the position of trying to account for these distinctions as if they were human-independent and natural, rather than human-dependent and synthetic.
It is in the realm of thought (mind) that we find both the world and our thoughts about it, while being forced to accept (contra idealism) that the world and our thoughts about it are one (insofar as idealism holds we cannot know the world beyond the mind). This does not erase the distinction between mind and world (a distinction that is entirely valid, and indeed necessary if we are to exist at all) but neither does it assert the distinction as anything other than a consequence of the very process that brings us and the world into being in the first place.