The RACI matrix is a formal way of establishing the role for each stakeholder/participant whenever multiple parties are involved.
We are doing it (Multiple Responsibles is possible)
The Golden rule (Only one Accountable for each task)
We know/share (Communication flows both ways – Consulted)
Want to know (One way only. Keep them, well… Informed)
In a nutshell:
R(esponsible) – Who is responsible for actually doing it?
A(ccountable) – Who has authority to approve or disapprove it?
C(onsulted) – Who has needed input about the task?
I(Informed, kept) – Who needs to be kept informed about the task?
A fast definition with an effective example is the Time to Market Nautical example.
Wikipedia is (also) your friend -check the RACI Matrix information.