Liberty and property are such closely related concepts that it makes some sense to say that they're the same thing. They are different sides of the same coin, if you will. Here's why.
What Liberty Is
Liberty is the absence of coercion. If you don't agree that this fully describes liberty, you probably will after I explain that I'm defining "coercion" very broadly. "Coercion" here is any time someone forces something upon you against your will.[1] This could take the form of a threat (I might threaten to punch you in the nose if you don't do what I want—that would be coercion) but it could also take a more direct form (I might actually punch you in the nose). The direct violence is coercion because you (presumably) do not want to have a broken nose, but I am forcing that upon you. The threat is coercion because I am threatening to force direct violence upon you in order to get you to do something you wouldn't otherwise do, so that take is being (by extension) forced upon you. Each of them, therefore, is a violation of your liberty.[2]
What Property Is
Property is the right to control an object. It's also known as ownership. If I "own" a piece of "property", that means I get to determine who gets to use it and for what. This can be understood from a behavioral perspective, a legal perspective, and from an ethical perspective.
From the behavioral perspective, what I own is simply that which I will defend more stubbornly than would otherwise be reasonable. That one probably requires more explanation.
In normal circumstances, in order to claim possession of a dollar bill, someone would probably be willing to give up an amount less than a dollar. This is reasonable for him to do because he will gain the difference between the value of the bill and what he spent to have it. However, if someone is willing to spend more than a dollar in order to have possession of that bill, this can not be justified in that way, and so requires additional explanation; why would he spend more than a dollar to ensure he has ownership of a specific dollar bill? One explanation is that he has designated that dollar bill as his property. If so, it makes sense that he'd be willing to give up more than a dollar to stop someone from stealing his dollar bill, because if he allows someone to steal it then others may realize that they can take whatever they want from him if they simply make it too costly for him to defend it. In this sense property is a strategy used to maintain access to some set of things that you believe you can defend with that strategy. From a behavioral perspective, to claim property rights over object is to attempt to communicate to others that, while they may be willing to take on some costs in order to take your object, you are willing to take on otherwise unreasonable costs in order to defend it. If this communication is successful then you will not actually need to take on these costs because other people will back down seeing that it's not worth it for them to try to take your property from you.
Then, there is the legal perspective. If the utility of these property rights is widely agreed upon, we may set up institutions specifically designed to help protect those property rights. In order to do so, these institutions will need to have definitions of who owns what. That set of definitions is called the law, and property, from the legal perspective, is simply what you own according to it.
Finally, there is the ethical perspective. From this perspective, that which you own is simply that which it is wrong to take from you. This one probably doesn't require further explanation.
You can probably see how these three perspectives of property rights come together. Property rights are a behavioral strategy which we codify into systems of law and into systems of ethics. What might not be so clear is how this all comes back to liberty.
How Liberty & Property Are Connected
Let's return to our simple definition of liberty; "absence of coercion." Remember that one example of coercion was me punching you in the nose. Now forget that one again, because it's too easy. Let's instead consider whether me eating an apple is coercion. If I eat the apple, you can no longer eat it. Am I forcibly taking away your ability to eat the apple, or am I simply exercising my liberty to eat an apple if I so wish?
The answer, of course, depends on whose apple it is. If it is my apple, I'm just exercising my liberty. If it's your apple, then I'm forcibly depriving you of your right to eat your own god-damned apple. If we ignore this distinction, and throw out any concept of property, then liberty would be an impossible standard to apply. Would apple-eating be an act of liberty or an act of coercion? Yes! It'd be liberty to the apple-eater and coercion to everyone else. It'd be impossible to say whether, to maximize liberty, we should prevent me from eating the apple or prevent you from preventing me!
In fact, in the absence of property rights, any act at all will create this conundrum. To make use of anything in any way is to prevent others from doing quite the same. We can both drink from the same stream, but we cant drink the same mouthful in the same spot at the same time.
So unless you want to say that every act is coercive (rendering coercion and liberty useless) there must be some class of objects in the world that you can use without it being considered coercive to everyone else. That class of objects we call your property.
I don't think I'm redefining concepts just to make them useful here, either (though that is a worthwhile thing to do sometimes). This actually seems to be how we often consider the concept of liberty intuitively. Consider our example about the punching of a nose. It is obvious that me punching your nose is coercive, but would it be obvious that it isn't coercive if it was me punching my own nose. It's from here we get the phrase "your right to swing your fist ends at the tip of my nose". It's the fact that it's my nose—the nose that I own—that makes the difference.
I don't know if I need to explain why it makes sense for you to be the owner of the nose attached to your face, while I'm the owner of the nose attached to mine (perhaps I'll do so some other time) but for now, I'm just making clear that liberty, to be useful as a concept, requires property. If the concept of coercion is to have any meaning, it must refer only to force used with respect to what someone else owns. If the conception of liberty is to have any meaning, it must refer only to the liberty to freely use your own property.
However, the initial claim I made was a little stronger than that, wasn't it? I said that it makes some sense to say that liberty and property are the same thing. In defense of that, let's consider what it means for liberty to be absolute, and what it means for property rights to be absolute. What that would mean is that only I get to determine what is done with my property—nobody else. I know I didn't say whether I was just describing absolute liberty or absolute property rights, that's the point.
What this all comes down to is this: Liberty is the right to do what you will with what is yours. Anything beyond that is doing what you will with what is not yours, which is not liberty, but tyranny.
You might prefer to call this "force or coercion" instead of just grouping it all under "coercion". If so, feel free to imagine that every instance of "coercion" in this piece was replaced by "force or coercion" and the argument should stand.
Perhaps you would prefer to define liberty as freedom from any physical impediment. You can define words however you want, but I submit that a better word from that would simply be capacity, or ability, since you're just describing what people are physically capable of doing. To define liberty this way would mean that if I'm physically unable to fly then I do not have the liberty to fly. This definition runs counter to how people usually talk about liberty. If someone claimed that he is being deprived of his liberty to fly we would tell him that no, he's perfectly free to fly if he wants to try, nobody's going to stop him, he's just lacking the physical capacity to do so successfully. In this example, at least, it seems that we implicitly consider liberty with the definition I outlined: the absence of coercion. In other words, in absence of the impediments placed on us by other people as opposed to the impediments placed on us by the laws of physics.
Not only is this definition more in line with our intuitive usage of the word liberty than the alternative, it's also more useful because it makes an important distinction that deserves its own word. If we don't use the word liberty to mean free from coercion, we'd just have to make up a new word that does mean that.
