Katarina Runes explained
There's one set of runes for Katarina on patch
11.10
that is the clear favorite for LoL players and pros alike. The best Katarina Runes on the position 
Mid are Precision as the primary path and
Domination as the secondary path with a pick rate of 48%. Besides runes you should take a look on Katarina Build and if you are interested in pro matches take a look at Katarina Probuilds. If you want to discuss
Katarina then you should visit the champion subreddit.
Primary path on Katarina
Precision improves attack and sustained damage on Katarina troughout the match. Most of high elo players – and our LoL pros in the the major regions – have agreed that
Conqueror is the best keystone rune to run on
Katarina. This keystone rune provides additional power in the later stages of a game. As soon as
Conqueror is fully charged, Katarina deals additional damage and gains life steal. This is usually followed up by taking
Triumph,
Legend: Tenacity and
Last Stand.
Triumph restores on Katarina a part of missing health and award bonus gold, if a champion is killed. Katarina gains extra Tenacity with every additional stage of
Legend: Tenacity. With
Last Stand you deal more damage while you are at low health.
Secondary path on Katarina
When it comes to your secondary path, most
Katarina players prefer to go with
Domination.
Domination improves burst damage and assassination tools on Katarina. On the
Domination path, the best runes for Katarina are
Sudden Impact and
Ravenous Hunter.
Sudden Impact increases your damage after dashing or being invisible. This is due to how easy it is to activate on Katarina with the amount of ways he has to dash, jump or going invisible. The additional lethality helps to take down the priority targets that much easier.
Ravenous Hunter is the final rune of the
Domination path. This rune gives some survivability during short fights and damage trades during the laning phase. The additional health is nothing to scoff at and can mean the difference between winning or losing a battle.