This "nest" is created by a male pufferfish for both courtship and for rearing young.
The male puffer fish uses its body and fins (a combination of pectoral, anal, and caudal -- see here) to break up the sand into fine particles and to move it around into the pattern seen above. It swims in channel-like (or furrow) patterns to create the ray pattern seen:
You can see a more complete video of this action through this BBC video on Youtube.
According to here and here this male puffer fish does all this to attract a female. National Geographic adds:
The circles, scientists say, are actually nests created by male pufferfish, which spend about ten days carefully constructing and decorating the structures to woo females. What’s more, this industrious pufferfish is thought to be a new species in the Torquigener genus, according to the study, published July 1  in the journal Scientific Reports....
When a potential female partner arrives on the scene, the male stirs up the fine sand in the nest’s inner circle. If she deems the nest, and the male who built it, satisfactory, she lays her eggs in the center of the nest and leaves.
Scientists are not sure why building intricate sand nests attract mates, but perhaps a larger, more-intricate nest (i.e., one that took a long time) could indicate to the female that the male is stronger or more fit.
All this effort does not stop at courtship however. Again from Nat Geo:
Once the female splits, though, it’s the male who does the parental chores: He remains in the nest until the eggs hatch six days later.