Usually, when people encounter "What is Property?" by Proudhon they find that instead of clear cut arguments Proudhon presents a series of legalistic indictments against the idea of property as defined by the French courts. It's pedantic and doesn't really easily admit analysis, but the basic idea nonetheless can be distinguished and is important. Everyone knows that the punchline to "What is Property?" is "Property is Theft." but looking at Proudhon's book there doesn't seem to be an easy way to get from his basic arguments, his way of approaching things, to the end point.
Well, the general thrust of it and why it matters has to do with the classical liberal idea that Proudhon is attacking and what his attack means. The classical liberal idea of property is that as long as a person has rightly earned it that they're entitled to whatever it is they have---even if there's a situation where some people accumulate extremes of wealth while other people just get by or don't get by at all. In the idea of classical liberalism if you level the playing field then people get what they deserve--the poor are poor because they deserve it, they're lazy or whatever, and the rich are rich because they've worked harder, which seems no doubt to be a cruel joke to people who have put in a lifetime of manual labor, but I digress. Property in this case doesn't just mean land, it means money and assets, in particular things like owning factories, or apartment complexes, or mines, or really large stores. The idea of Proudhon's is basically this: if you can prove that property rights, that the idea of property rights, is really inconsistent, that it's not a clear cut idea, then you can assert that the people who own these things really don't have a right to them. Instead, they belong to the community, or to society as a whole.
Property is theft because in Proudhon's argument people really don't have a right to own things that give them a huge advantage over others. People don't have the right to personally own things that are used by the community as a whole, that exist for the benefit of the community, and are run by members of the community. It's like saying why put one person in charge of a community enterprise and let he or she get the profits from it and use them in whatever way they want?
Proudhon's line of attack goes something like this: take my apartment complex, for instance. It's huge, there's several hundred apartments there. I rent an apartment. Some entity owns the apartment complex as a whole. Now, why do they own it? Because they paid millions of dollars to buy it. But who did they buy it from? Someone else, who probably put up the money to have the place built. But where did they get the money to do that and what let them do it? They went to a bank with a business plan for a piece of land that they bought from someone. The bank approved their plan and gave them a huge loan. But where did the bank get the money? It just had it, the bank has money from people in the community in savings accounts and such and they used some of that money to make a loan. But why is it that banks can take the community's money and decide where to give it in order to fund business projects? Well, it's because it's a private enterprise, people deposit the money there, they choose to deposit the money there, and then the bank decides what to with it, based on somewhat ethical decisions, hopefully. But it's the community's money, why is it that the bank is an independent entity and not under the control of the community? There's no really good answer to that. The basic excuse is that some entrepreneur decided to start a bank, which kind of dodges the point.
At the base of it, if you trace the origin of property rights back to the start in this fashion you come to the conclusion that what people are using to create their businesses is really community property.
Property is theft because it takes what was originally communal property and puts it in private hands.
Now, Proudhon's particular arguments have no bearing on the Anglo-American legal system. The basic type of argument outlined above holds, but if you look at what exactly Proudhon argues about in particular in "What is Property?" you find that it attacks the notion of property as defined in the Napoleonic Code, which was the reformed legal system in France after the Revolution. This tradition of legal thought is foreign to Ango-American Common Law ideas, including those of property. In a way Proudhon was arguing against property in a system that was more predisposed than that of the U.S. or England to have ideas of property deflated. The idea of absolute property rights does not exist in continental Europe. If you own something, there's always autmatic qualifications on what exactly ownership means in relation to society. Unfortunately in the U.S. the idea is out there that property rights come first, before society, that they're primal: I have this and no one can or should be able to tell me what I can or can't do with it; and anyone who wants to legislate regulations for me will have to struggle like they're pulling teeth to get me to comply. Ok, that's in relation to the State, but it dodges the question of where you got your property from and why you have it.
You can assert the rights to the property that you own now all you want but the fact is that you got it from somewhere. But at some point this argument breaks down because not all property is things like capital goods, which is what the example I used dealt with. People work and save up to buy stuff. Their buying stuff isn't automatically oppressive. It's just saving up and buying stuff. Proudhon saw this and, in fact, wasn't against small amounts of property; it was the big property that he was against. At some point your mom and pop store becomes something more than a mom and pop store; once it has enough influence in the community and ceases to be a small business it transforms into something else, something that people usually express with the term 'Corporation', no matter if that's technically true or not. When it becomes a corporation that's when it starts to be a problem and that's when private ownership becomes an issue. That's when it should come under the control of the community and not be in private hands anymore.
Abolish corporate personhood, restrict the charters if you can, but in the end hedge them in so much that they no longer work for themselves but work for you instead.
Then there's the issue of where the money ultimately comes from. Sure, if I have a specific white collar job and rake in tons of money I get that money because I'm associated with Capital, I'm an employee of the people who own the Corporation, but what makes the corporation in this country so prosperous? Part of it is that it depends on the exploitation of the undeveloped world, what used to be called the third world. If the Corporation was in a country that didn't have access to foreign labor, and it couldn't get that labor, then even though I as a hypothetical white collar employee would get more money than the people working for for the Corporation on the blue collar side I wouldn't get half as much as I get in being allied with a corporation that get's money due to third world exploitation.