Jesus' promise concerning whatever is bound or loosed can sound mysterious when the expressions are detached from their Jewish setting. The paired terms belonged to the language of authoritative decisions about what was forbidden or permitted.
Matthew uses this language in connection with the keys of the kingdom and later in teaching about the community's handling of discipline.
Jewish teachers had to interpret Scripture and apply its commands to concrete circumstances. "Bind" and "loose" could function as terms for prohibiting and permitting. The expressions could therefore carry the idea of authoritative judgment rather than physical tying and untying.
The exact scope of Jesus' promise must be interpreted from Matthew's context, but the idiom itself belongs to a recognizable world of teaching and communal authority.
Knowing the idiom prevents the passage from becoming an undefined promise that believers may verbally "bind" anything they dislike. The language concerns authority exercised in relation to the kingdom and the community Jesus is forming.
The historical background therefore focuses attention on responsibility: decisions made under Jesus' authority are not casual preferences but matters of serious interpretation and communal judgment.