[NearAP]

From their website (step 3 of how it works)

TransferWise converts your money at the mid-market rate and matches you with people sending in the other direction. That's why it costs so little.

My understanding - after you've given the money you want to transfer to TransferWise, they find someone in your destination country who wishes to transfer money to the country where you are (kind of like a swap). This way, they cut off the banks and their fees and charge you a lower fee.

[jotm]

That's how I understood it, but then I thought "what if there's no one in that country?" Do they use their own funds or does the recipient wait several weeks.

I imagine it's the former, but at the time I just used SWIFT - rather expensive, but guaranteed to work everywhere.