Property is important because it’s inextricably tied up with more basic concepts like rights and procedural justice.
Procedural justice is about adherence to strict, transactional, rules of behavior, or procedures, while distributive justice is about how value ends up distributed among people as a consequence of whatever behavior. I hold that distinction to be analogous to the epistemological distinction between analytic and synthetic knowledge. Both procedural justice and analytic knowledge are simply about following the correct steps in sequence from a given starting point to whatever conclusion they may imply, analytic knowledge following just from the assigned meaning of words and procedural justice following just from the assigned rights that who has over what (which I analyze as identical to the concept of ownership, i.e. to have rights over something is what it means to own it). Likewise both distributive justice and synthetic knowledge are about the the experience of the world, synthetic knowledge about the sensory or descriptive experience of the world and distributive justice about the appetitive or prescriptive experience of the world.
Meanwhile the distinction between perfect and imperfect duties, which was introduced by Immanuel Kant, is roughly the distinction between specific things that we are obliged to always do, and general ends that we ought to strive for but admit of multiple possible means of realization. I reckon that distinction, in turn, to be analogous to the epistemological distinction between a priori and a posteriori knowledge, because just as a priori knowledge comes directly from within one's own mind (concerning the kinds of things that can coherently be believed) while a posteriori knowledge comes from the outside world, so too perfect duties come directly from within one's own will (concerning the kinds of things that can coherently be intended) while imperfect duties comes from the outside world.
Many liberal or libertarian political philosophers have at least tacitly treated these distinctions as largely synonymous, with procedural justice, matters concerning the direct actions of people upon each other and their property, being the only things about which anyone has any perfect duties, on their accounts; and conversely, distributive justice, matters concerning who receives what value in the end, being at most subject to imperfect duties, if even that. But I argue that, just as Immanuel Kant showed that the distinction between analytic and synthetic knowledge was orthogonal to the distinction beween a priori and a posteriori knowledge, so too the distinction between procedural and distributive justice is orthogonal to the distinction between perfect and imperfect duties.
At the intersection of matters of distributive justice and perfect duties lies the moral analogue of the synthetic a priori knowledge that Kant introduced. While that synthetic a priori knowledge is about imagining hypothetical things in the mind and exploring what sorts of things could even conceivably be imagined to be, this intersection of perfect duty and distributive justice is where I place the traditional moral concept of "The Golden Rule": if you cannot imagine it seeming acceptable to you for someone else to treat you some way, then you must find it morally unacceptable to treat anyone else that way.
This is very similar to but subtly distinct from the matter of property rights — of not acting upon something contrary to the will of its owner (including a person's body, which they necessarily own, i.e. necessarily have rights over), which lies in the traditional intersection of perfect duties and procedural justice — because it does not rely on any assignment of ownership, but only on experiential introspection; in much the same way that synthetic a priori knowledge is very similar to but subtly different from analytic a priori knowledge, in that it does not rely on any assignment of meaning to words, but only, again, on experiential introspection.
And of course, just as I hold there to be a category of analytic a posteriori knowledge as well, I also hold there to also be an intersection of procedural justice and imperfect duties as well, which is of utmost importance. For while distributive perfect duties are obligatory (as obligation tracks with perfect duty, and omissibility with imperfect duty), for that same reason of them being internal to the will (hence perfect duties), but not in terms of publicly established relationships of rights (hence distributive), they are not interpersonally relatable, and so are only a matter of private justice, not public society.
The only obligations that can be treated publicly are those phrased in terms of property with assigned ownership, procedural perfect duties; but those in turn depend on the procedural imperfect (and thus omissible) duties of assignment of such ownership.
When we assign ownership of certain things to certain people, which is to say that the will of those people controls what it is permissible to do to or with those things, we get procedural matters of perfect duty, where we no longer need to actually do the imagining of what it would feel like to be another person being acted upon in some way, and can just deal in abstract claims. This is where we enter the realm of property rights, things that are right or wrong just in virtue of who owns what and what they do or don't want done with it, regardless of whether it actually inflicts hedonic suffering or not.
But this kind of justice in turn depends on another kind of imperfect duty, just as distributive perfect duties depend on distributive imperfect duties. Procedural perfect duty, justice in virtue of who owns what, depends on the assignment of ownership of the things in question, and that is not something that is itself a matter of perfect duty, but only imperfect duty. Nobody inherently owns anything but themselves; rather, sociopolitical communities arbitrarily assign ownership of property to people, and could assign it differently. People own what other people agree that they own, and so long as everyone involved agrees on who owns what, that is all that is necessary for that ownership to be legitimate, to conform to the procedural imperfect duties of who owns what.
But when people disagree about who rightly owns what, we must have some method of deciding who is correct, if we are to salvage the possibility of any procedural justice at all; for if, for example, two people each claim ownership of a tract of land and are each wanting to deny the other the use of it, they will find no agreement on who is morally in the right to do so because they disagree about who owns it and so who has any rights over it at all. Such a conflict could be resolved in a creative and cooperative way by dividing up the land into two parcels, one owned by each person, that would permit both people to get the use that they want out of it without hindering the other's use of it. Or the same property can have multiple owners, so long as the uses of the property by those multiple owners do not conflict in context. (Initially, all property is owned by everyone, and in doing so effectively owned by no one; it is the division of the world into those people who own the property and those who don't that constitutes the assignment of ownership to it.)
But if no such cooperative resolution is to be found, and an answer must be found as to which party to the conflict actually has the correct claim to the property in question, I propose that that answer be found by looking back through the history of the property's usage until the most recent uncontested usage can be found: the most recent claim to ownership that was accepted by the entire community. That is then to be held as the correct assignment of ownership, the imperfect duty of this procedural matter, in much the same way that satisfying all appetites constitute the imperfect duty of distributive matters.