also: るすのま
expression, noun which may take the genitive case particle 'no'
during one's absence; while away
Used as a noun phrase or adjectival expression to refer to the period when someone is not present. Often followed by に to indicate 'while someone is away'.
留守の間に荷物が届いた。
A package arrived while I was away.
彼の留守の間、私が犬の世話をした。
I took care of his dog during his absence.
留守中 is a more common and concise way to say 'during one's absence', often used in set phrases like 留守中によろしくお願いします. 留守の間 is slightly more explicit and can be used in similar contexts.
Compound of 留守 (absence) + の (possessive particle) + 間 (interval, period). The reading あいだ is standard; ま is an older, less common reading for 間 in this context.