The bill itself is simple, and adds a new section 18A to the BORA, with the UN-recognised language: "Everyone has the right to a clean, healthy, and sustainable environment". If it passes, then laws would have to be assessed for consistency with the right, and laws could be declared to be inconsistent and the declaration referred to Parliament so the law can be corrected.
What this would mean in practice would depend significantly on the standard of scrutiny adopted by the courts and the degree of latitude they grant to the executive. On that front, the courts have already said that climate change policy requires the highest level of scrutiny because of its impacts; less significant issues will likely have a lower standard (just as the right to be free from torture has a higher standard of scrutiny than the right to be free from discrimination). Being inconsistent with the right is likely to be a high bar to cross. So as with the BORA, a lot of the actual impact would come from the pre-legislative scrutiny, forcing the government to run a stricter environmental ruler over policy before introducing legislation, and from the courts interpreting existing legislation in order to be consistent with the right. And given how much change that process has led to in e.g. public order or search and seizure law, having it happen to environmental law is likely to be significant. So I'm hoping this gets drawn from the ballot next year.