Catching the same species in a row in Let's Go, Pikachu! and Let's Go, Eevee!
A catch combo grows each time you catch the same species back to back. Higher combos add shiny rolls, and a Lure and the Shiny Charm add more on top. The bonus stops growing at a combo of 31.
Running from a battle or moving to a new route does not break it.
The combo bonus only applies to the next spawn of your chained species after a catch. If you stop catching at 31 and just wait, new spawns go back to normal odds. Keep catching to keep the bonus.