>>21830047It's basically left over terminology from PokeRadar.
In this case, the "chain" refers to how many times you've encountered and defeated/captured a pokemon using the DexNav, either through directly searching or it randomly popping up in the shaking grass. (Some people say you only have to actually initiate battle and can run away too and have the number go up.)
When your DexNav locks onto the shaking grass, it'll display in the upper right of the screen how many times you've encountered it. As this goes up, so does the chances of egg moves, hidden abilities, and items being encountered, and their level increases as well.
People seem the think it might also increase shiny chance and getting multiple egg moves, but we have no real confirmation on those.