Once you reach Ascension Phase 2, you are able to level up your characters' talents (skills). Levelling them up will increase their overall effectiveness since it ups their multipliers. To level them up, you need some talent level up materials, that looks like books, which can only be obtained by going to the talent book domains.
Additionally, you will need some monster material drops as well. Different characters will be using different materials, and these are obtain somewhat easily by defeating monsters in the world. At higher levels, you will need higher rarity versions of the drops, increasing your adventure rank increases your world level, thus getting better loot.
You can also use the crafting table, that's available in cities like Mondstadt/Liyue, to use the lower tier items into higher rarity ones. It always requires 3 to make the upgraded version of it.
How to Farm Talent Level-Up Material
There are only 2 talent level up material domains right now: Forsaken Rift, and Taishan Mansion. Their drop rewards changes each day, so make sure that you do these on the days that drops the book that you need.
Different characters uses different named books. As the talent level increases, you'll need more of them, and also higher rarity versions of those talent books. Try to plan out and prioritize your units to manage your resin, since levelling talents can get quite costly.
You can tap the materials in-game to find which enemy drops certain items. Unique enemies like Geovishap Hatchling, and Fatui Skirmishers can be located easily by going to the adventure handbook, then in the "bosses" tab, find the enemy and tap the "Navigate" button.
Side note: Geovishap Hatchling is available in Liyue region, so you'll have to switch it to view in Liyue region in the "bosses" tab.
Quick list of characters that uses certain items, so you'll know what to save up for certain characters.
See the link below for how to defeat enemies guide.