I hadn't heard of the phrase 'legacy systems' before, and apparently it's most often used in relation to the computer world. However, according to Wikipedia, it may also be used to describe human behaviors, methods, and tools. For example, timber framing using wattle and daub is a legacy building construction method. In other words, the phrase applies to the use of old methods (or in computerese, old programming systems) that are still functioning alongside more recent ones.
We tend to think that the computer world continues to upgrade at every point - certainly for us end-users that seems to be mostly the case - but for those who work in the basement, as it were, where all the programming is actually done, it seems there are a host of possibilities. Programmers can continue to use old ways of programming alongside new ones without blinking an eyelid.
But it has some issues, which is why places will advertise legacy system programmer jobs these are for people who know how to program using the old systems. It's kind of like having an old tradesman on the job with you who can do things that the modern machine doesn't do nearly as well.
The Wikipedia article tells us that NASA still uses a lot of 1970s technology because it's too expensive to replace. But NASA's not alone in this: many companies would find it prohibitively expensive to replace their computer systems. So they live with the consequences.
I sometimes think I'm a person in the legacy systems mode: I much prefer to play the piano when there's a choice between a piano and a keyboard. For me, so far, there hasn't been a keyboard that's successfully duplicated the touch and feel and weight and much more of an actual piano. But then I'm a Luddite in all sorts of things...!