When we say that a species like cockroaches is ancient, what does it mean exactly? Does that mean that cockroaches haven't evolved for a long time? But isn't evolution always occurring? So is that because they haven't evolved as much and are very similar to their ancestors, ie they had a "very slow rate of evolution"?
It depends on the context.
first "cockroaches are ancient" is different than a species being ancient, cockroaches are not a species but a group of species with a similar morphology and ancestry (similar to a clade).
It can mean they are mrophologically similar to their ancestors. Which is very different than saying they have not evolved. It means the pressures on the linage have not favored much in the way of morphological change. Some shapes just work well,(or reach equilibrium) and once you reach it the morphology don't change much even when other things are changing.
It often means that the split between the lineage in question and other groups is old. example, you could say mammals are ancient for instance because the mammal lineage split off the rest of the amniotes 275 millions years ago. They have changed a great deal since then but the groups as a whole goes back a long time. the issue here is these splits are minor when they occurred, like any other specialization event, but look big due to human constructed categories.
But it can also mean that the lineage has not undergone a specification event for a long time, It has changed but has not left behind any offshoots, this is the rarest case but can happen.
Note however this is a phrase the media like to throw around when it doesn't have a solid scientific definition, it is a qualitative contextual statement. They often have little understanding of its meanings. They also often fail to clarify which they mean, and often fail to properly define the "thing" being ancient.