Ardent Coins and Celestial Coins are special currency, they are given once per day after first Invocation. You can spend them in Vault of Piety accessible after clicking icon next to invocation icon near minimap.
Ardent Coins are given for fist invocation each day and you wont loose them until you spend them, but after visiting Vault of Piety you will notice that more coins will give you better rewards, so choose you goal and collect enough coins.
Celesial Coins are also given on first invocation on daily basis, but you can have maximum 7 of them, and if you skip one day and you won't invoke all collected coins will be lost. Celestial Coins are also currency in Vault of Piety.
You can only exchange Ardent Coins for Seals of different kinds in Vault of Piety, there is no other option to exchange this currency.