Someone sent a message to a peer-to-peer discussion group and remarked, "This is critical. I'm a DRI at the moment and have some issues to fix."
The term DRI was new to many people on the mailing list (including me), and while others on the mailing list helped to solve the person's problem, I also learned that DRI stands for designated response individual or designated responsible individual, depending on whom you ask. This is the person who is responsible for monitoring and replying to email messages sent to a hot issues mailing list. For online services, it's the person responsible for dealing with live site issues.
From what I can gather, teams that use this model rotate the job of being the DRI through the members of the team, so that each person on the schedule serves as DRI for a set period of time (typically a day or a week). The DRI may also be responsible for running various tools at specific times. Each team sets its own rules.
Other teams have come up with their own name for this job. Another term I've seen is Point Dev. On our team, we call it the Developer of the Day.
Bonus chatter: I bought this hat back in the day when the stitching was done by hand on a specially-designed sewing machine. Nowadays, it's computerized.