I think other comments in this thread have done a great job of pointing to some common sources and their resolution. I'll mention a few things I've found interesting in discussing the question over the years:

1. I am often the source of unexpected stress.

Sometimes it's something I said (or didn't say). It may be something that gets interpreted in a way I didn't expect. Simply clarifying what I meant or discussing the matter further usually resolves the more serious aspects of the issue.

2. It's frequently a great way to address issues that improve performance or productivity.

This is not the point. But a lot of times I'll have a developer, especially a younger developer, say something like, "I'm really stressing out over this user story I'm working on." Then we have a higher level discussion on design or scope or something else that's blocking them.

I also learn important business-related stuff I might not have known otherwise. "Wait, you're working on that? Why are we working on that?" Or, "Oh, cool, I didn't realize we we're doing that." And then we discuss that with the goal of taking the stress out of things.

3. Personal issues do come up.

Occasionally my teammate will ask something like, "Are we talking about stuff here in the office or home, too?" I'll usually respond anything goes but note that my ability to help is largely constrained by things I can control here in the office. But that includes, as other have suggested, a more flexible schedule, days off, or referrals to others that may be better qualified to help. A manager's ability to assist is going to depend to a certain extent on the culture and policies of the organization. But as others have pointed out, sometimes the most important thing for the person you're talking to is just being heard out.

I'm a little surprised by the level of skepticism exhibited in the response to my original comment. I mean I understand it. But if your response to your manager asking this question in a 1-on-1 is to immediately question your manager's motives, I'd recommend looking for another job. I'm not saying it will be easy to find one, especially one with an organization or supervisor who is necessarily any better. But as this thread shows, they are out there. And if that is your reaction and you're not exploring your options, I think you're ignoring a huge signal regarding your wellbeing.

I'd also say if this is a question you think it would help to discuss with your manager and you're not sure how to bring it up, maybe ask them the question.

Finally, my point in mentioning this is to hopefully encourage more leads and managers to ask this question or some variant of it and pay attention to the issues raised in this thread. If your reports are unduly stressed out, you're not getting your best performance out of them. You're not really doing your job.

And to clarify this isn't an official metric in any sense. It's really just an icebreaker to get to underlying issues that may affect performance and wellbeing. 3 is a step on the way to 2. 2 is optimal in my view. But if someone is a 1 and they're getting their work done, all the better!

I'm hoping it's a corrective to a lot of the braindead KPIs and metrics and just generally toxic practices that are out there. But, yes, something like that IT Crowd clip is a potential unintended consequence of this question in the wrong organization. To the extent you can make things better for yourself and others, please do so.

If I can help anyone, you can probably guess my gmail address. Feel free to drop me an email.