Okay, so this sounds like it's a method of programming that is entirely incompatible with anything I work on.
What sort of thing would it be useful for?
The kind of things I do tend to have maybe several hundred thousand floating point values that exist for maybe a couple of hundred thousandths of a second, get processed, get dealt with, and then are immediately overwritten with the next batch.
I can't think of any reason why I'd ever need to know what they were a few iterations back. That's gone, maybe as much as a ten-thousandth of a second ago, which may as well be last year.
It is useful for the vast majority of business processing. And, if John Carmack is to be believed, video game development.
Carmamack's post explains it - if you make a series of immutable "variables" instead of reassigning one, it is much easier to debug. This is a microcosm of time travel debugging; it lets you look at the state of those variables several steps back.
In don't know anything about your specific field but I am confident that getting to the point where you deeply understand this perspective will improve your programming, even if you don't always use it.