Evolution is made up of two parts, broadly speaking: random variation and natural selection. (And sexual selection but I’m leaving that aside for now)

Random variation doesn’t slow down, it’s effectively always bubbling away making the next generation look and function slightly differently. These are effectively copying errors when the genetic code is replicated.

Natural selection can appear to slow down, or halt entirely. This is where organisms try to survive in the world long enough to reproduce, “may the best man win” so to speaks (all genders evolve, it’s just a phrase). As time goes by, the species either becomes better suited to its environment or goes extinct. And there is a limit to how well suited it can become (if nothing else, evolving can in principle get stuck at a dead end).

Such animals are called “living fossils”, and I believe alligators are an example of this. There are some plants also which have barely changed for millions of years, because they are very well suited to their environment and any variation tends to make them worse.