In order to be allowed to walk more than 2000 cubits outside the city limits on Shabbat, an individual must arrange for an eiruv teḥumin that will shift his central living space to the edge of the boundary, effectively moving his 2000-ama limit over to that spot. This is accomplished by placing food on the boundary and intending to “make Shabbat” in or near that spot.
The Mishna (32b) teaches that if the individual does not plan to actually camp out in the spot of the eiruv where he placed the food, he needs to be able to theoretically access the food as Shabbat begins – which is when his “Shabbat residence” is established – and eat it there. Thus the Mishna rules that if the eiruv is placed in a tree above ten tefahim (=handbreadths), the eiruv is not valid, since above ten tefahim is considered a reshut ha-yahid – a private domain – which cannot be accessed from the ground. When it is placed below ten tefahim, then it is accessible from the ground and the eiruv is valid.
In the Gemara (33a), Rav Yitzhak the son of Rav Mesharsheya explains the Mishna’s case to be where the branch of the tree in which the eiruv was placed grew out more than four amot from the trunk, and the individual planned to establish his “Shabbat residence” at the tree’s trunk. Furthermore, the branch begins below ten amot and grows to a height above ten amot. Since his intention was to establish his Shabbat residence on the ground near the tree trunk, if he placed the eiruv in the upper branches of the tree the eiruv would not be accessible to him at the onset of Shabbat and would, therefore, be invalid.
To the Gemara’s suggestion that perhaps the eiruv can be accessed, were the individual to take it from its private domain position above ten amot and bring it directly via the tree to the place where he is making Shabbat, the Gemara responds that the tree under discussion is one that is used by the public to rest and rearrange loads that are being carried. Therefore this tree has an unusual status in that it is considered a reshut ha-rabim – a public domain – because of its popular use.