ESV is the abbreviation for "Egg Shiny Value". It's a hidden individual 4 digit code attributed to every egg. With the help of a program called KeySAVᵉ these hidden codes can be read, which allows players to aim for specific shiny Pokémon easier. If a TSV (Trainer Shiny Value) matches an ESV (Egg Shiny Value), then the Pokémon inside the egg will hatch shiny. I suggest that you look up further information on the internet since the threads and guides there will be able to give you a much more detailed explanation.