Something to do with rolling up the sleeves of the flying suit.
Normally the brief would be off-the-cuff but with the cuff round the elbow we have an elbow brief.
It can also be used in the debrief phase when the sleeves are normally rolled down. In this case a gentle push with the elbow into the other party's ribs is frequently sufficient admonishment for an inappropriate remark or act during the flight. Hence elbow debrief.
Where the debrief needs to be more robust a straight right to the nose is usually sufficient to reinforce the point.