Electro Sigils are a vital resource in Genshin Impact as they are used to increase rank with the Sacred Sakura Tree. The Sacred Sakura Tree can be found at the top of Mt. Yougou at the Grand Narukami Shrine.
You will need Electro Sigils to offer to tree, allowing you to level up and gain all manner of bonuses. Just like in the other regions, these elemental sigils are not easy to come by and may take some time to collect.
The first source of Electro Sigils is opening chests. Any time you see a chest as you explore Inazuma, you should try to open it, including figuring out any puzzles that may have been locking it. All chests have a small chance of dropping Electro Sigils.
You can also earn Electro Sigils by finishing the new Domains in the region, as some will offer a one-time reward for competition. You can also earn Electro Sigils by collecting Electroculus and bringing them to the Statue of the Seven.
Remember, that the current islands that make up Inazuma are just a small part of the overall continent, and a lot more will be coming in the future, so you will not be able to fully rank up the Sacred Sakura yet.