Tower Runes are items that you can equip to your Towers to give a stat boost.  Once you have a Rune equipped, ALL Towers of that type are affected.  They can increase your damage, speed, range, slow, stun duration, and poison.  Additionally, Tower Runes can increase the max uses on certain Tower types, add more targets, and increase your chances for piercing armor and crits.  A Tower Rune can have one or multiple effects.  

The amount of stat boost is based on the Tower Rune’s Star value.  Star values determine the Rune’s starting stat boost, and they range from 1 to 5.  Star values can be increased only through certain chests and rewards in the game.

The Runes themselves have levels.  You can increase a Tower Rune level with Dust.  Dust can be obtained from chests and as rewards from other areas of the game, like the Campaign.