Exodus 6:14–27 is important because the story that is being told is interrupted by this genealogy.
Moses and Aaron have gone to the Pharaoh (Exodus 5:1). But their mission seems to have been unsuccessful: the Pharaoh is not letting the people of Israel go, but instead heaps on more work for the slaves to do. Then God commands Moses to go again (Exodus 6:12, Exodus 6:30). After that, God sends Moses and Aaron together (Exodus 7:1–2) and starting from that moment, they continue to visit Pharaoh together; together they appear as the shepherds of Israel (Psalm 77:20).
In the next chapters (covering the ten plagues and the exodus) the story is not interrupted again.
14 These are the heads of their fathers’ houses: the sons of Reuben, the firstborn of Israel: Hanoch, Pallu, Hezron, and Carmi; these are the clans of Reuben.