In Path of Exile, currencies play a central part in the game's ecosystem. Getting familiar with them can be quite daunting at first, so in this guide, we aim to explain the most relevant currencies there are.
Firstly, it must be noted that generally, currency items are interchangeable with each other for example, two orb of scouring can be exchanged for one orb of regret at some in-game npc, and also players are free to trade with each other in a free economy.
For the sake of clarity, we will break down currencies by the act the player is introduced to them, then explain the other currencies that aren't connected to given acts.

Act 1:
Portal scroll: An item that can be used to create a single-use portal from where you are to your current town area.
Scroll of wisdom: Used to identify unidentified items.
Orb of transmutation: Turns a normal item into a magic item giving it up to one prefix or one suffix over the base affix of the given item.
Orb of augmentation: Adds a new modifier to a magic item.
Orb of alteration: Used to reroll magic items' modifiers to more desirable ones.
Armourer's scrap: A currency item, that upgrades an armour's quality.

Act 2:
Chromatic orb: Used to reforge the color of sockets on an item.
Jeweller's orb: Used to reforge the number of sockets on an item.
Orb of fusing: Creates a link in between sockets on an item.
Orb of scouring: Removes all modifiers from an item.
Orb of regret: Gives the player a refund point on the passive skill tree.
Blacksmith's whetstone: A currency item, that upgrades a weapon's quality.

Act 3:
Orb of alchemy: Used to upgrade a normal item into a rare one.
Orb of chance: Upgrades a normal item into a random rarity (magic, rare or unique).
Glassblower's bauble: improves the quality of a flask.

Important to know that there are vendor recipes for various currency types, for example vendoring a six socket item will give you seven jeweler orbs, you can check the official wiki for the game for the rest of these.
Now, that we covered the most basic currencies let's talk about some other important currency items you will come across in PoE that usually can't be bought from npcs and you get them mostly as a random drop or encounter reward.

Exalted Orb: Augments a rare item with a new modifier.
Chaos orb: Reforges a rare item with new random modifiers.

The two above are the staple trade currency and players usually price their items and other currency items in either depending on the value (exalted orbs being more valuable). There is also the divine orb which lets the player reforge the random numeric values of modifiers on an item.
The following one is said to be the rarest item in the game, many players never finding a single one in their entire carrier and it is the Mirror of Kalandra, a currency item capable of creating an exact copy of a rare item - thus duping it so you can see why it is so rare and of course, very valuable. 
Other currencies you will encounter in the game include end-game boss currencies, such as the Crusader's exalted orb dropped by Baran, the crusader, which adds crusader influence and a new crusader modifier to a rare item.
Also, it's worth mentioning that there are more currencies you will find in the game besides the ones already mentioned in the article. For example, league currencies that are specific to given contents like legion splinters or rogue markers.
We hope our guide helped you give a clear overview of the important currency items in PoE.