First introduced in Pokémon Yellow, Pokémon following you has always been a much requested feature. After only appearing in HeartGold & SoulSilver and Let's Go, Pikachu! & Let's Go, Eevee!, the feature makes a return in Pokémon Sword & Shield with the Isle of Armor.
Once you have completed Mustard's trials, he will give you the allowance of taking your Pokémon for a stroll. From this point on, the first Pokémon in your party slot will be out in the field when you're in the Isle of Armor. This only applies in this location and can't be done in the Wild Area or any cities of Galar.
There is one bonus. Previously, the maximum happiness of a Pokémon without use of Pokémon Camp was 160. If you walk around with your Pokémon following you in these areas, it can reach 180 without Pokémon Camp.
The Pokémon following you will mostly be scaled correctly, though the largest of Pokémon will scale down slightly. Your Shiny Pokémon will also appear as shiny in the overworld.
Following Pokémon - Deactivating the Feature
If you do not wish to use this feature, there is a way to disable it. In the Master Dojo, if you go to the Kitchen you will find a Poké Kid with a Pikachu. Talk to them and they will ask if you like it or not. If you say no, the Pokémon will return to its Poké Ball.