Runes are shattered fragments of the Elden Ring, and are similar to Souls from Dark Souls wherein they act as the main form of currency in the game. They are primarily gained by killing enemies or from consumable items.

Uses: Leveling Up

We can summon Melina at Sites of Grace to leveling up. Leveling up will involve increasing attribute points, which will affect other stats like Attack Power, HP, FP, Stamina, Defense, Carry Weight and, more.

Uses: Enhancing Weapons and Gear

We can use at Smithing Tables or Blacksmiths. Using a Smithing Table allows players to give their items a stat modifier of only up to +3, but Blacksmiths can go even further.

Uses: Buying and Selling Items

We can use it to interact with Merchants. Merchants, found across the Lands Between, sell useful items like Spirit Ashes or Crafting Kits at the cost of Runes.

Rune Farming Guide: How to Get Runes (Souls) ?   Elden Ring New Rune Farm | Rune Glitch After Patch 1.08!

NOTE: 

When you die, you leave behind a mark and drop all the Runes that you have been carrying. You can recover a portion of your dropped Runes by heading back to the place where you died, looking for your mark, which appears to have shimmering branches sprouting from the ground, and interacting with it.

If you die once more, without retrieving your Runes, you will create a new mark, and the previous sign will disappear, losing all the Runes it held.