You can do two things. Either use them for crafting items or exchange them for goods that can be sold in Auction House. Be aware that by selling the crafted items, you might get much more gold.
To exchange the spirits, there is an NPC in Shrine of Seven Stars named Krystel (Alliance side). There is a similar NPC for the horde side. It’s a female pandaren that is standing on the platform there.
I’ve noticed that the best deal is to buy “Prismatic Scales”. A stack of 20 can be sold for around 200 gold, but this depends on the realm’s population. I play on a medium populated realm. The other goods that you can get from exchanging spirits of harmony are much cheaper when selling them but the best thing to do is to check the Auction House prices first.
If you play a lot of PVP, you can exchange 4000 honor for 1 spirit of harmony. You can make quite a good amount of gold.