Gold/Plat. Regular currency. 100 Bronze is 1 Silver, 100 Silver is one Gold, 100 Gold is one Platinum (Plat). Players can trade with it, regular stuff cost this currency. You can't buy gear with it, except starter gear and few BoE items on Auction House.
Renown. You get it for doing any group content or any content in group. It is mostly good for Housing decor and buying High Runebags.
Elder Gems. You get them after level 50 instead of experience. You can buy AMP and AP points with it, and unlock 3rd and 4th LAS. Hard cap is 2000, but with using tier 5 contract bag or weekly EG quest - you can go through the cap. Having more than 2000 is not recommended, because if it is exactly 2000 - all experience will be converted into regular currency (gold).
Glory. You get it for any PvE 5+man content. Good at start for buying some glory gear after clearing Ohmna raid boss. Good for Superb/Divine Runebags.
Triploons. You get them from killing bosses and minibosses in raid Redmoon Terror, you can buy gear and Risen Runes with it. If you have at least one, check this guide: https://origination-jabbit.com/index.php/Guides/Entering-redmoon-terror/?
Prestige. PvP currency, you get it for doing PvP content and for killing players in open world. You can buy and improve PvP gear with it.
Omnibits. You get them for doing any content that is giving you experience. There is soft limit of guaranteed drops, it is 120 for f2p players and 360 for subscribed players. With this currency you can buy almost everything in cash shop. Best way to spend them is on Service Tokens for runeing, keys and costumes.
Crafting Vouchers. It is currency for crafting, you can buy recipes and crafting stuff with it.
Service Token. Currency which is used to replace gold cost sometimes. Best use is on Runecrafting to get slot you want instead re-rolling with gold (which can cost a lot of gold if you are unlucky). Best way to obtain is to buy them in cash shop with Omnibits.
Fortune Coin. It is donate "Random Box" currency. You get some random cash shop items from boxes from Madame Fay. Mostly mounts, decor and costumes.
Promissiory Note. Currency you get from Contracts. You can buy Rune Foci and Runebags with it. And it is good for pushing your reputation when you need AMP/AP/Costume/Decor from reputation vendors.
Character Boost Token. Donated ability to create character on instant level 50. It will have a bit of gold, runecrafting materials and itemlevel 70 gear for both specs (2 ilvl higher than basic starter gear, but all this gear will be raplaced by ilvl 90-100 from contracts and expeditions in few days anyways).