The question that our Gemara has focused on is whether a household object is considered part of the structure of the house itself, which would then be seen as part of the house and would be sold with it, or if it is considered separate from the house, in which case we cannot assume that the seller meant to include it in the sale.
Whether something is “connected” is significant in Jewish law not only in questions of monetary issues, but in other areas, as well. A question of tumah ve’tahara – ritual defilement and purity – is an example where such a question is important, and our Gemara brings cases from that realm of halakha to help establish certain principles in our situation. One general principle in the laws of tumah ve’tahara is that things that are connected to the ground cannot become tameh – they cannot become ritually defiled. The Gemara brings a Mishna from Massekhet Kelim (15:2) which teaches that a daf shel naḥtomin – a baker’s board – that is affixed to the wall will not become tameh according to Rabbi Eliezer, but the Ḥakhamim rules that it can become tameh. The Gemara brings this in an attempt to establish that according to Rabbi Eliezer, such a board is perceived as part of the structure of the building and therefore is considered “connected to the ground.”
The case of a daf shel naḥtomin is understood by most rishonim as referring to a piece of wood on which the baker kneads and prepares his dough. The Rashbam suggests an alternative explanation, that it is a display shelf on which the baker arranges his wares for sale. In either case it is a simple wooden plank. This is significant since the Gemara eventually rejects the suggested approach that Rabbi Eliezer views a simple connection as making something considered “connected to the ground,” rather they argue that the status of the shelf as peshutei keli etz – an unformed piece of wood – is what allows it to keep from becoming tameh.