Bitcoin is digital currency. It is used as a store of value. At the time of writing 1 BTC is equal to 1451 USD.
You can send bitcoins from one wallet to another. Hence, this can act as a payment system for domainers.
Suppose you bought a domain from somebody. The first step is to pay for the domain. You normally use Paypal or an escrow service to send the money across. You can use Bitcoins instead to pay the seller.
The transaction is almost immediate or might take a few minutes.
In order to own bitcoins, one needs to have an account in one of the bitcoin exchanges in your country. A simple Google search will help you find the right one. They will provide you a digital wallet and it will have a unique wallet ID (public key). You can use fiat to buy bitcoins there and also you can convert your bitcoins to fiat to get it credited in your bank account.
Some of the advantages I see in bitcoin transactions for domainers:
1) You could probably avoid the hassles and delays associated with Paypal, Wire, escrow.
2) You could probably save a good amount of money in transaction fees. Bitcoin transaction fees are very minimal.
3) It is fast. Sending bitcoins is like sending an email.
4) There is no border specific or value specific restriction to send bitcoins across.
5) You don’t depend on a bank or a financial institution to send your money across.
6) Do it with a click of a few buttons.
7) In case you want to keep your wealth in bitcoins you can do that. Bitcoins are an asset class and is limited in quantity. Its price appreciates as demand grows. Just take control of your private keys by using cold wallet or hardware wallet if you are holding for long term.
8) You could use the bitcoins you received for other purposes like recharges, bill payments, paying your employees in another country etc.
9) You can save dollars by going for a bitcoin based escrow service.