The Torah prohibits carrying on Shabbat between a public domain and a private domain or for more than 4 cubits in a public domain. However, the Torah permits carrying within an enclosed "private" area. Public domains are typically non-residential areas including streets, thoroughfares, plazas ("open areas"), highways, etc. Private domains are residential areas, and originally referred to an individuals home or apartments that were surrounded by a "wall" and can be deemed to be "closed off" from the surrounding public domains. The rabbis of the Talmud developed a means to render a larger area as a private domain by surrounding it. Such an enclosure is called an "Eruv", more specifically "Eruv Chatzayrot" or Sheetufe M'vo'ot. The Hebrew word "eruv" means to mix or join together; an Eruv Chatzayrot (henceforth just "Eruv") serves to integrate a number of private and public properties into one larger private domain. Consequently, individuals within an Eruv district are then permitted to move objects across the pre-Eruv public domain-private domain boundary.
The laws of Shabbat distinguish four domains, which are defined both by the manner in which each type is enclosed and the manner in which it is used. The first is a makom petor, or exempt area. An exempt area is one that is at least three hand-breadths higher than the ground and whose area is less than four hand-breadths by four hand-breadths. There are no limitation upon transferring an object to or from an exempt area on Shabbat. The second type is a semipublic, or "neutral" area, neither strictly public nor private, known as karmelit (e.g., fields and oceans). The third type of area is the private domain, which in order to qualify must be very clearly set off and defined (e.g. the interior of a house). The fourth type of area is the public domain, an open area always used by the public. Included in this category are highways, deserts, and forests. The Shabbat laws regarding the permissibity of transferring objects from one domain to another are explained in the Talmudic tractate Shabbat of the Order Mo'ed.
Eruvs serve to create a larger private domain. In order to consider an area a private domain, the area must cover at minimum an area of about 12 square feet and must be somehow demarcated from its surroundings, either by a wall of some sort or by virtue of its topography (that is, it is either all higher or all lower than its surroundings).
The problem was that it is impractical to build a continuous solid wall around a community. However, the rabbis noticed that doors are permitted within walls, and that a doorway consists of two parts: the vertical members and the lintel on top. In fact, a wall may have quite a few doors, and still be considered to enclose an area. In the limiting case, there are many doorway openings and having very little of solid wall remaining.
This is what happens in an Eruv. The door post function is fulfilled by telephone (utility) poles (serving as vertical members), with the lintel being cables strung between the poles. However, for a door post/lintel combination to be acceptable, the lintel must rest directly above the top of the doorposts. Note that this is not the typical approach in utility poles, where the cable is attached either to the side or to a member held away from the pole. To address this, there is often a thin rod attached onto the pole to serve as the door post "surrogate" ("lechi"). Additionally, the line that serves as the lintel needs to be the lowest of the lines on the pole. If it is not, then it is necessary to string a new length of line between the affected set of poles.
In areas where the poles and lines do not exist, new pole/line combinations must be erected. These added poles must of course be high enough so as not to impede traffic. Fences may be used as part of the boundary without modification; however, if the ground is eroded beneath the fence to any significant degree, the space must be filled in. Lastly, all the areas to be enclosed must be "residential areas," or areas suitable for residential areas. It is not permitted to include bodies of water [lakes, streams, and ponds, although reservoirs currently in use as drinking water sources are permitted without modification), and cemeteries. Such areas must be excluded from the Eruv by closing them off (either by not including them in the Eruv area, or by encircling them within the Eruv).
The Eruv is generally designed by encircling a community with a continuous string or wire. There are numerous regulations concerning the placement of this wire. Those who live in and use an Eruv have an obligation to ensure the Eruv is intact before taking advantage of its presence. Usually, there is a group that maintains the Eruv that provide such information, and conducts weekly inspections.
Note: There are other types of Eruv than that described above. Specifically, there is an Eruv Techumim, which may be used to define the "home" location for Shabbat in order to alter the permitted travel area.
Note that Eruvim are typically found in traditional communities. Eruvim are less of concern to Conservative Jews, and are not of significance in Reform. However, the non-Orthodox groups generally do not protest Eruv (although some secular Jews do), as it enhances Shabbat for those that do observe the laws concerning carrying.