HP, ATK, and DEF are pretty simple to understand and can be pretty self explanatory, but Elemental Mastery is a stat that is unique to this game. Thankfully, the game does give more explanation about this when we tap the "Details" button when we view a character.
From this screen we can see that Elemental Mastery's purpose is to increase the damage of elemental reactions only, and it also shows the increased amount. Naturally, this means that EM stat is best on characters that can cause a lot of elemental reactions.
Understanding Elemental Reactions
If you forget, or want to know more about elemental reactions, you can view the game's description by going to the main menu, then select "Archive" -> "Tutorials."
For a brief understanding of elemental mastery and their reactions, we can see in the Elemental Mastery stat when we view the details that EM affects 8 different reactions differently, and they are separated into 3 parts:
Vaporize and Melt.
Overloaded, Superconduct, Electro-Charged, Shattered, and Swirl.
Crystalize.
Elemental Mastery increases the values of ALL the reactions, but not equally. This is because the damage of most elemental reactions (Overloaded, Superconduct, Electro-Charged, Shattered, and Swirl) are only based on your character's level, EM, and the enemy's resistance. Increasing your attack won't change the damage of those reactions. Vaporize and Melt reactions simply amplifies your damage, so it's already much more effective on its own. The damage dealt is also based on the stats of the character that triggered the reaction.
Upon causing an Overloaded, Superconduct, Electro-Charged, or an Electro-infused Swirl reaction, increases Base ATK by 20% for 12s.
Elemental Mastery are mostly from artifacts or weapons, but there are also other ways to increase it like Sucrose's passive that gives EM to your team. Characters like Lisa can also get EM as the bonus stat for levelling them up.
Only the Hourglass and Crown piece of artifacts can have Elemental Mastery as their mainstats, but EM can be a substats on any artifact piece. Use the filter on the bottom and select "Elemental Mastery" for an easier time when trying to find them.
If you want to focus on EM from the artifacts, you can consider using Instructor, or Wanderers Troupe for their set effects.
Who to use it for?
Elemental Mastery is a good on characters that can trigger elemental reactions often. However, do keep in mind that not all elemental attacks will apply elemental status on an enemy. This is because applying an element has an internal cooldown, which is not shown in the game. Lisa's attack deals Electro damage, and it will apply an Electro element, but her next normal attack won't apply electro element because it's on cooldown, and thus won't be causing a reaction with each attack.
A skill with multiple hits and low hitting numbers are a good candidates for characters that can benefit a lot from Elemental Mastery. This ability doesn't deal a lot of damage, and while not all of the discharge will trigger a reaction, it does hit multiple times. Increasing your EM means that you are relying on the damage of the reaction, instead of the ability itself. This can result in higher total damage output, compared to focusing solely on attack. Just be sure to also level up the character that will be triggering the reactions to increase the damage.
Another example of a character that can be good with Elemental Mastery. In most cases, unless your bring a character to your party solely just to proc a reaction, it's still better to just increase attack since it increases the damage of your other abilities and normal attack as well, and the same applies to characters like Venti or Lisa. Go with attack% mainstats on your artifacts, and EM on substats as an optional one to consider.
Support DPS like Beidou, Xiangling, or Sucrose are examples of other characters that can be good with Elemental Mastery.