There are several ways stability and insight work together.
Stability practice itself, such as counting the breath, inevitably gives some insights. The first one is usually how active the mind is, and how easily attention is distracted and lives its own life outside of conscious control. Then other things, such as how distractions has to do with attention getting absorbed into stories, and how beliefs related to these stories makes it more likely for attention to be absorbed into them. (They seem more real, more important, and they are also identified with so not recognized as just thoughts very easily, until maybe afterwards.)
Stability of attention also helps more explicit insight practices, first by allowing attention to stay wherever it is put for longer, and also by generally calming the activity of the mind so there are fewer hooks for distraction.
And insights allow for more stability of attention. We learn to see through how beliefs are created, as it happens, and recognize thoughts more easily as just thoughts. And this lessens the tendency for attention to get absorbed on the inside of thoughts, which in turn allows attention to more easily stay where it is put.