Polities are groups of people who come together to make decisions and enact their will. These are given various names depending on their form, structure, intent, scale and scope. Therefore they are variously called "countries", "towns", "clubs", "cabals", "mafias", "federations", "treaties", "unions", "associations", "companies", "phyles", "tribes", "counties", "regions", or any other of a number of different terms.
The reason we use the word "polity" in Wasa2il is that it is the most generic term we could find. It says nothing of the form, the structure, the intent, scale or scope of the group of people, nor does it preclude anything. Using the word "group" could work too, but it lacks the imporant factor that there is an intent to make decisions and enact will.
In addition to consisting of a group of people, a polity will have a set of laws the group has decided to adhere to. In an abstract sense, membership in a polity grants a person certain rights and priviledges. For instance, membership in a school's student body may grant you the right to attend their annual prom, and membership in a country (i.e. residency or citizenship) grants you a right to live there and do certain things there, such as start companies. stand in elections, and so on.
Each polity has different rules - these are also called statutes, bylaws or laws - which affect the polity on two different levels.
Firstly, there are meta-rules, which describe how rules are formed, how decisions are made and how governance in general happens. Wasa2il has to be flexible enough to accomodate the varying meta-rules of a given polity, otherwise the polity may decide that Wasa2il isn't useful to them. Sometimes these rules are referred to as "rules of procedure" or "constitution", depending on the type of polity which is using them.
Secondly there are external rules, which are the decisions the polity makes which don't affect its internal decisionmaking process.
It is hard to talk about a term completely in the abstract. We can describe its features, but that only gets us so far. So let's look at some of the things that can vary from one polity to another, and then take a few examples in each.
The scope of a polity determines the range of things that the polity concerns itself with. The scope may be a geographic region, a set of ideas, a particular part of social activity, or a common interest of its members.
La Casa Invisible is a social center in Málaga, Spain, which works in the Málaga region to promote ideas of social cohesion, autonomy, and democracy. It operates a café, a book store, a music hall, and various other projects, each of which could be considered a sub-polity of the social center itself. The scope of La Casa Invisible's actions is mostly bound to decisions regarding the social center itself, and the activities that take place within it.
The Union of the Comoros (Udzima wa Komori) is an island nation to the east of Africa, just north of Madagascar. It has a population of 798.000 people living in an area of 2.235km². The scope of The Comoros as a polity is the land and national waters they control, their airspace, and their foreign trade, defense and other agreements they are party to. As such, they have municipal sub-polities, and are a member of the African Union, Francophonie, Organization of Islamic Cooperation, Arab League and Indian Ocean Commission superpolities, amongst others.
The scale of a polity determines how large it can be expected to become. Some polities are specifically structured with intent to grow, while others intentionally try to stay at a constant size.
Muff Divers is a diving club in the village of Muff in Ireland. It claims to be the fastest growing diving club in the world, most likely owing to its name.
A polity is created around intent. Some polities intend to take over the world, others intend to make the nicest cupcakes in all of the land. Some polities intend to send people into space, and others intend to track down and arrest criminals. Polities have all sorts of motives and intents.
On the most basic level, a polity's intent is a description of what it intends to do. This has nothing to do with whether the polity has the ability to do it, or whether anybody or anything - such as another polity, or the laws of physics - stand in their way.
Representative democracy, direct democracy, participatory democracy, dictatorship. There are lots of terms which describe the structure of a polity. In one sense, it refers to where in the structure of relations between people the authority lies. In a dictatorship, one person has ultimate authority, although he may choose to grant some authority downstream to trusted advisors, who in turn have trusted advisors, and so on. In a fully egealitarian system, each individual is equipotent, meaning he has an equal ability to everybody else to instigate decisions - however, it depends on the structure what ability the individual has to actually complete the decision making.