There are both economic and military implications of the conflict over these islands.
Economically, the islands may contain rich deposits of gas and oil. If they do, they could become a very important source of revenue for the country that ended up with control over them.
Militarily and politically, the conflict has the potential to seriously disrupt stability in Southeast Asia. All or part of the islands is claimed by no fewer than six countries. Importantly, one of those countries is China, which has been acting aggressively to try to assert what it sees as its rights. Because China is involved, there is the potential for the US to get involved if it thinks China is becoming too expansionist. Therefore, the conflict could lead to extreme tensions and even military action that could include countries that do not even claim the islands.