A festival's publicity is ready, but nobody booked the venue. Each organizer thought someone else owned that task. A responsibility matrix puts work on one axis and people or roles on the other, turning those assumptions into something the team can inspect.
The grid connects work packages with the people or resources assigned to them. More elaborate variants distinguish several kinds of involvement, but the basic mechanism is simpler: make responsibility visible across the whole undertaking.
The festival team could map venue booking, ticketing, volunteer scheduling, and equipment to named owners. Empty rows expose missing ownership; a person's overloaded column exposes a capacity problem. Several names on one task may indicate useful collaboration or unresolved ambiguity about who closes the loop.
The matrix does not grant time, skill, or authority merely by displaying a name. Assignments need to be accepted and consistent with what people can actually do. It should also remain small enough to use and change when the work changes. Its purpose is a shared understanding of commitments, not a bureaucratic artifact that looks complete while the people listed in it remain surprised.