That looks like a LED lamp, where the bulbs are integrated into the fixture and are not replaceable. You will probably need to replace the whole fixture.
Just in case, look to see if there is a part number, possibly on the back of the fixture (against the ceiling).
EDIT: I googled the part number on the circuit board (Samsung e473485) and it is called a LED Downlight. You can find plenty on online hardware stores by searching for that phrase.
I personally don't like how non-serviceable those are (especially since, AFIAK, the electronics tend to fail before the LEDs will ever fail). Consider your replacement options.