Runes in Doom are perks that you can equip by completing rune trials throughout the single player. They start appearing on the level Argent Facility and stop appearing at the level Lazarus Labs. There are a total of twelve runes and you can equip up to three on the Praetor Suit, and if you upgrade your suit to show all icons this will also show you the locations of the Runes on the map. The challenges themselves can be quite tricky and require some patience, but if you're really stuck I found that taking a break and coming back always helped
(video credit to PowerPyx)
Vacuum - Argent Facility - 0:05
Increases the range for absorbing dropped items (ammo and health)
Dazed and Confused - Argent Facility - 0:47
Increases how long enemies remain in a stagger state.
Ammo Boost - Argent Energy Tower - 1:23
Increases the amount of ammo gained from items and enemies.
Equipment Power - Argent Energy Tower - 2:16
Increases the effectiveness of Equipment items.
Seek and Destroy - Kadingir Sanctum - 2:51
Glory Kill enemies from much farther away.
Savagery - Kadingir Sanctum - 3:49
Perform Glory Kills faster.
In-Flight Mobility - Argent Facility (Destroyed) - 4:27
Provides a significant increase in control over in-air movement when doing a double jump.
Armored Offensive - Argent Facility (Destroyed) - 5:04
Glory Kills drop armor.
Blood Fueled - Advanced Research Complex - 5:51
Move faster for a short time after performing a Glory Kill.
Intimacy is Best - Advanced Research Complex - 6:41
Increases the damage resistance of staggered demons, making them more Glory Kill friendly.
Rich Get Richer - Lazarus Labs - 7:24
Firing your standard weapons will not cost Ammo when you have 100 or more Armor.
Saving Throw - Lazarus Labs - 8:23
Get one chance to survive a death blow and recover health. This resets on death.