The Torah at Exodus 16:29 shows that keeping the Sabbath included all Israel going to their tents on that occasion. Rest involved being stationary in a single location, the home. The Israelites are to stay in their place on the Sabbath day. Each person has a place, defined as four [square] cubits (enough for a burial plot), and may move from that place for the distance of two thousand cubits in any direction.
The law in the Talmud Tractate Eruvin focuses on the verses, Exodus 16:29–30, that link the act of eating with the place of residence: “See! The Lord has given you the Sabbath, therefore on the sixth day he gives you bread for two days; remain every man of you in his place; let no man go out of his place on the seventh day. So the people rested on the seventh day.”
The combination of the double supply of bread for Friday and Saturday and the admonition to remain in one’s place leaves no doubt that (1) one stays home, and that (2) home is where one eats. Here is the topical outline of the tractate.
I. The delineation of a limited domain
A. Forming an alleyway into a single domain
B. Forming an area occupied by a caravan into a single domain for the Sabbath
C. A well in public domain
II. The eruv and the Sabbath-limit of a town
A. The eruv: A symbolic meal for establishing joint ownership of a courtyard or for establishing symbolic residence for purposes of travel on the Sabbath
B. The eruv and violating the Sabbath-limit
C. Defining the Sabbath-limit of a town
III. The eruv and commingling ownership of a courtyard or an alleyway
A. The eruv and the courtyard
B. Areas that may be deemed either distinct from one another or as a commingled domain so that the residents have the choice of preparing a joint eruv or two separate ones
C. The shittuf and the alleyway
D. Neglecting the eruv for a courtyard
E. An eruv for more than one courtyard
F. The eruv and the area of roofs
IV. Public domain in general
The tractate addresses the problems: How can Israelites on the Sabbath move about from one private domain to another? How can the community so arrange matters that shared and common ownership of private domain secures for all parties the right to carry within the space held in common?
One answer is for the community to prepare a symbolic meal, a meal that legally commingles ownership of property, because where one eats, there one resides. By sharing property among all the partners in the meal, the right to said meal and property is shared by all. All householders thereby commingle their property rights, so that joint property will then form a single common estate from the various private domains.
Another answer is to establish a boundary around the entire set of private domains, one that, like a wall, forms of them all a single property. The medium by which the one or the other procedure is carried out is called an ‘eruv, a medium of commingling, thus referring either to the symbolic, shared meal or to the equally fictive demarcation line, as the case requires: a meal of commingling, or a boundary-marker for commingling ownership of private property.
from the Wikipedia article Eruv
There are 39 categories of activity prohibited on Shabbat. On Shabbat (Jewish Sabbath), the Torah forbids moving an object from one domain to another, no matter its weight or purpose.
There is no Biblical source in the Law of Moses that explicitly prohibits carrying on Sabbath. However, the Rabbis of the Talmud find two sources of the prohibition. “Let no man go out of his place on the seventh day” (Ex. 16:29). This verse is in the context of collecting the Manna bread. The Rabbis said, “Let no man go out of his place with a receptacle in his hand.” According to this, the Manna cannot be collected on Sabbath because it cannot be carried into the Israelites’ homes.
Second, “So the people were restrained from bringing” (Ex. 36:6). This verse explains that the Israelites refrained from bringing further materials for the construction of the Tabernacle.
The Rabbis say that this event occurred on Sabbath, and not just because no more supplies were needed, but also because the people were not allowed to carry those supplies to the Levite camp. The Rabbis derive the prohibited actions of Sabbath from the actions that were performed to construct the Tabernacle. Based on this, one explanation is that since this verse is written in context of the Tabernacle, it is appropriate to derive further that the people ceased to carry on Sabbath.
According to Torah law as understood by the Talmud, this prohibition encompasses three actions:
Moving an object from an enclosed area (such as a private home, public building, or fenced-in area) to a major thoroughfare,
moving an object from a major thoroughfare to an enclosed area, or
moving an object more than four cubits within a major thoroughfare.
To prevent confusion over exactly what constitutes a major thoroughfare, the rabbis expanded the ban to any area that was not fenced or walled in.
An eruv surrounding a community in Jerusalem has an additional, rabbinic prohibition, which Jewish tradition ascribes to the religious court of King Solomon, forbids carrying in any area that was shared by the occupants of more than one dwelling, even if surrounded by fences or walls. But, in this case of areas surrounded by walls, carrying was allowed through the use of an eruv. The eruv consists of a food item - in general bread - that is shared by all dwellers. By means of this shared meal, all the dwellers are considered as if they were living in a common dwelling, thus exempting them from the added prohibition.