Otobi - Jump

...In some regions, gifts in general are called tobi, but this is said to be derived from tabe, meaning a gift from the gods, and the gift-giving behavior of the Japanese is rooted in ancient beliefs. The customs of sending food to those absent from a meal, such as sending food to those who are absent, and of wrapping food for attendees to take to their families, and of sharing food, are ways of expanding the effect of eating together. The customs of returning a gift container called otsuri, otobi, or otame, leaving a little bit of food behind, or returning a piece of paper or matches inside, are thought to be remnants of the etiquette of eating together by passing around a piece of food, just like the custom of leaving a little bit of rice when replacing it. It is said that the custom of adding bamboo grass or nandina leaves to food gifts is a remnant of the old days when leaves were used as tableware, or to ward off evil spirits.

*Some of the terminology explanations that mention "Otobi" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…また贈物一般をトビと呼ぶ地方もあるが，これは〈賜（た）べ〉に由来し神からの賜物を意味すると説かれており，日本人の贈答行為は古来よりの信仰に根ざしたものといえる。会食に欠席した者に食物を送り届ける〈送り膳〉や出席者にもその家族へ食物を包み持たせるならわしまたおすそ分けなどは共食の効果を広げるものであり，オウツリとかオトビ，オタメと称し贈物を入れてきた器に食物を少し取り残して返したり半紙やマッチなどを入れて返すしきたりは，御飯を少し残してお代りする習慣同様，一つの食物を移し回していただき合う共食の作法を残したものとみられる。なお食物贈与にササやナンテンの葉を添えるのは古く葉を食器として使った名残とか魔よけのためといわれている。…

※「オトビ」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典 第２版について | 情報