Computer controlled enemies have chance to drop different levels of runes which can be embedded into socketed equipment. Each socket can be embedded with one rune. Runes can be taken down for a second time use, though there is chance of failure.
When a rune is embedded into a weapon, it will give the weapon the effect of the rune. For example, when Water Strike rune is embedded into a weapon, the weapon's Water damage will be increased.
The damage from the rune is expressed as either 'X per 3 seconds' or 'Strikes for X points' - both actually work the same (non-obvious) way. The former is new new description, the latter the old one. Although the damage is per 3 seconds, it's accumulated and only delivered when you make a normal attack - so it you attack once every 6 seconds, you'll be doing an extra 2xX elemental damage on each hit. This strange mechanism has, presumably, been used to limit network traffic as it avoids the need for he runes to use a explicit attack once every 3 seconds.
It is suggested that, when embedding runes, you attempt to specialize in a particular element. This is because it's easier for a focused attack to overcome a target elemental defense (assuming most characters and monsters have fairly evenly distributed elemental defenses).
How can you embed a rune into a weapon? Edit
See Upgrading Items.