What is it?
Most common type of currency in the game for trading. Similar to gold coins from some other RPG-s.
You can get Chaos Orbs by vendoring a full set of rare items with item level between 60 and 74 to an NPC. A full set consists of weapons/shield, two rings, an amulet, gloves, boots, helm, body armor and a belt. You can check the item level of an item for this by hovering over the item while holding the Alt key.
If you sell an unidentified set of items as described above, you get two Chaos Orbs, if any of the items is identified, you get one Chaos Orb.
Some players prefer the identified recipe as you can find out if the item is good before selling it, but most items are useless, so it might be better to sell them unidentified for this purpose, because then you get twice as many Chaos Orbs.
Chaos Orbs are mostly used for trading - selling and buying items and other currency.
If you have a bunch of Orbs of Alteration for example and want some Orbs of Fusing, then it makes most sense to first sell your Alterations for Chaos Orbs and then use those to buy Fusings. You might be able to trade directly at a worse rate, but it is often best to think of other currencies as "items" and Chaos Orbs as "money". Other types of currency also often used for trading are Orbs of Alchemy for cheap items and Exalted Orbs for expensive items.
Chaos Orbs are also used for rerolling mods on a Rare item. This is an unreliable way to get an item with mods that you want. Unless you have several hundred chaos to spend, it is not recommended to try to get a good item this way.
Chaos Orbs are sometimes used on Rare Map items, when it has undesirable mods. For example, you use an Orb of Alchemy on a Map to turn it Rare and make its loot better, but it gets the elemental reflect mod. You would die to elemental reflect, so you use a Chaos Orb on it, to reroll the mods, keeping it Rare, but making it less deadly.