内弟子とは師と寝食をともにし、あらゆる武術のノウハウと秘伝を伝える制度だ。

、。

A 'live-in disciple' is a system where the disciple shares meals and sleep with the master, and every bit of martial-arts know-how and secret teaching gets passed on.

Literal

Live-in-disciple [as-for-とは] master [and-と] sleep-food [obj-を] together [do-し], every martial-arts [gen-の] know-how [and-と] secret-teaching [obj-を] pass system is.

The sentence is a definition: AとはB = 'as for (the thing called) A, it is B.' 内弟子 ('inner disciple') — someone who lives with the master rather than commuting — is a traditional apprenticeship model in martial arts, tea ceremony, rakugo, and similar arts. 寝食を共にする is a fixed idiom literally 'to share sleeping and eating,' i.e. to live together intimately. あらゆる is a classical-flavored 'every, all,' stronger than すべての. 秘伝 ('secret teaching') preserves traditional knowledge transmission as a flavorful Japanese cultural concept.