Intentionality= The direction within mental processes.
Example: Think about your wife. Are your thoughts directed at her? If so, you have an example of intentionality.
Not a spooky definition, and quite honestly, not at all hard to understand. It is a special kind of teleology, which is, in aristotelian definitions, a directedness toward something (e.g. the ball to the ground because of gravity, medicine toward certain receptors in order to achieve certain effects etc.). Teleology, at its most basic form, can be found in every material process. Intentionality concerns directions within mental processes. The question, and the difficulty for naturalistic philosophers, is to eliminate the intentionality and bring it down to a mere material process.
This is also why in the context you bring it up in your last comment
you´re actually not making, but missing the point. The intentionality you are elaborating on is meaningless, as long as we don´t assume that the mind is a computer and therefor reducible to the material process (which is also not a premise, but it must be argued for).
This is also why I don´t recognize you as having made any explanation about which intentionality (as if there were anything other than the specific defintion) you believe in. Because you haven´t made any meaningful statement with that definition in mind, as far as I can see.
Simple: Does direction in your thoughts exist? Do you have the ability to think about something? Then intentionality exists and the metaphysical consequences from that premise follow. If not, then not, then there are other consequences.
This is what I have been outlining my points with, which is why your confusion is a mystery to me (or maybe not, remember the Rosenberg-quote?).
The rest follows tomorrow, particularly about your misunderstanding of the different ontological status between software and hardware.