What is this light? How can I replace / fix it?
This is an LED fixture. The idea is that it should last 60,000 hours (?). When it burns out you simply replace it. See the comment from @Tyson. The only other thing you can do is to check and make sure it is getting power when you turn the switch on. 

You might be able to get a warranty replacement if you know the manufacturer or the place it was purchased.

Sorry I can't help you further.