Lol, I can try, I find it a bit difficult to understand myself sometimes. I think I have to start a bit before the actual squatting:
Holland is a very small country with many inhabitants (16 millions) compared to it's size. It takes aproximately 3 hours to drive from east to west, and four hours from south to north in you could drive in a reasonable straight line and have no trafficjams.
Considering this, you would probably not get surprised if I told you that housing is a big problem here, and quite expensive. I have seen families squized in on amazingly little place, even though I wouldn't necessarily consider them poor.
The governement here is trying to build more appartments to make it easier for young couples and people with less income to get their own place. But things take time, and to encourage "rich people" or companies owning buildings that is inhabitable but not in use to do something about this property, they have made it legal to squat buildings. And if you can prove that the building has been standing empty for 1 full year, and you manage to stay in there for 24 hours without being kicked out, you have the legal right to live in that building. It might be very difficult for the owners to get rid of you legally.

This of course sounds like a good idea, only that even if the building has not been empty for a full year, it might still be squatted, and it will take a considerable amount of time to get rid of the squatters. In addition, it might take a lot more than one year to get started with a project, espescially if the property is very big, costly or a monument. And it might be difficult for you to find people you can trust to take care of the buidling in a proper way (that is, make sure all rooms that has water in them are heated, make sure it looks inhabitated, notify the owner if there is something wrong-for example a leakage). The buildings might be unhandy to live in, you might not know how long it will be empty, etcetc.

To lift away most of these problems for owners that has other things to consentrate on than standing in front of the door watching for squatters, certain companies are registering people who wants to live in these kind of buildings. They are then contacting owners of buildings that look empty, and offers to find someone who wants to live there. Both the owners and the renters (anti squatters) are paying this company a certain sum of money. The owners are paying for the company to take care of the subletting, make sure the people take care of the building etc. The anti squatters are signing a cotract with the company, usually a regular rent-an-apartment thing, with a few exceptions.

The company has the right to kick out anti squatters with 2 weeks notice, and they give no guarantee that you will get a new place to live (although if they think that you are a decent person they will do their best to try). On the other hand, you pay next to nothing for living there (and things like gas and electricity is included in the price). The standard and size of the building vary greatly, but they do not rent out anything that is not really possible to live in (has to have water and heating for example).

I think that explain most of it, but if you wonder of something, just ask

Charlie