While some halakhot are clearly stated in the Torah, others are barely hinted at, and are derived through a variety of methods of exegesis. Our Mishna lists different laws and comments about how clear the sources are for each of them.
Heter nedarim – the court’s ability to free someone from vows that they have taken upon themselves – are described as “flying in the air” in that they have no solid source in the Torah.
Hilkhot Shabbat and Hagigot (the laws of the Shabbat and the requirement of certain specific sacrifices on pilgrimage holidays) are among the examples of laws that are considered “mountains suspended by a hair” in that they have some source in the Torah, albeit a weak one. The Jewish legal system, the rules of ritual purity and the laws of forbidden sexual relations are examples of halakhot that are well grounded in lengthy passages in the Torah.
The Turei Even explains the distinction between those halakhot that “fly in the air” and those that “suspend by a hair” as depending on the extent to which the source for the law is unknown. Those that are considered “flying in the air” have no true source in the Torah; they are derived from a hint. Heter nedarim for example, does not appear anywhere in the Torah. It is derived from another law, one that allows a father to annul the vows of his daughter, or a husband to annul the vows of his wife, under specific circumstances (see Bamidbar chapter 26). On the other hand, halakhot that “are suspended by a hair” do have a solid Biblical foundation, just that the Torah does not spell out what the requirements are in a comprehensive way. The concept of Shabbat, for example – including the idea prohibiting creative work on that day – is clearly written in the Torah in several places. Nevertheless, the 39 specific categories of work that are forbidden are derived from the activities of the Tabernacle, and are not mentioned in the Torah.