I2P Name Registry is a domain name registration service for I2P. Hostnames in I2P aren't globally unique. I2P Name Registry doesn't act as "central authority", it only provides a way to publish hosts as an easy means of access to them. You can read more about how I2P naming works in the official docs.
To find out how we're registering and publishing hosts, look at FAQ page.
I2P Name Registry also provides a jump service. For accessing hosts through it, use urls like http://inr.i2p.re/jump/example.i2p.re. I2P since 0.8.3 gives possibility to add a custom jump-servers. Go to the i2ptunnel eeproxy configuration page and add http://inr.i2p.re/jump/ to "Jump URL List" section.
If you are running an eepsite or another service and want a human-readable domain name for them, consider registering it.