The way this is most often talked about is in terms of tasks. Which tasks fit in which quadrant? Deciding that allows you to get more done, because you're working on those tasks that are most important to reaching your goals, while avoiding the trap of those tasks that only seem important yet demand immediate attention (quadrant 3 - the danger zone).
Personally, I've found this to be a helpful tool, particularly when dealing with requests from others, and helping others filter requests made of them. But in order to use the tool well, you have to know what your priorities are before you evaluate your tasks. Only then can you answer whether a task is important or not. The language you'll most see attached to this tool is one of goals; if a task helps you achieve your goals, then it's important.
In this matrix, urgency is secondary to importance, and rightly so. But importance is secondary to focus. Another way of saying it is that productivity only matters if your priorities are clear. Think about it in terms of a runner in a race; the fastest runner in the world won't win if she's running in the wrong direction. She can run as urgently as she wants, but it's not going to help her win the race because she's not focus don the actual finish line.
Unfortunately I think many of us allow ourselves to invert the matrix, where urgency becomes primary. We allow ourselves to feel good about doing a bunch of stuff, and it doesn't really matter if it's actually important stuff or not. Checking things off the list gets to matter more than being confident that we're working with the right list to begin with. We live life primarily in quadrant 3, which feels right, even though it's not. That's what makes it a dangerous place to live.
And this is where a time of unexpected and enforced disruption to our lives can aactually lead us towards more health. We can take the time to evaluate whether we've got the right list. And then, we can use a tool like this matrix to help us check the things off the list. At that point, we won't just feel productive. We'll actually be productive, because our output will be focused. Even if we do fewer things (and that's almost guaranteed right now), having healthy and clear priorities will bring our "getting stuff done" into the place where it belongs: as a servant, not a master. Productivity is led by priorities, not the other way around.
If only it were so easy to do as it is to write.