The Supreme Court of India, in a case concerning the protection of the Great Indian Bustard, ruled that the right against climate change is a fundamental right. Fundamental rights are rights guaranteed by the constitution (such as the rights to equality and personal freedom) or ‘interpreted’ as such by the Supreme Court (so far, only the right to privacy). They apply to all Indian residents, rather than only citizens, and cannot be removed except by constitutional amendment. The court also set up an expert panel to monitor the protection of the bird, and urged governments to speed up expansion of solar power.
There already are laws dealing with specific issues. So I guess the main advantage of making this a fundamental, rather than just a legal, right would be that it would bind governments. This will support challenges to laws diluting environmental protections, as well as allow lower courts to pass orders on issues where no specific laws already exist.