The concept of 'Matters of National Environmental Significance' (MNES) is a political construction that does not necessarily reflect all nationally significant issues. As at 1 January 2021, there are nine defined areas:
http://www.environment.gov.au/topics/heritage/heritage-places/world-heritage-list
The Commonwealth can add new matters to this list by regulation. The list must be reviewed every five years to see whether further matters should be included. If a proposed action is likely to have a significant impact on any of the areas, it may require Commonwealth approval before it can begin. It is illegal to undertake such an action without that Commonwealth approval.
Not all actions that affect a matter of national environmental significance need Commonwealth approval. The activity must be likely to have a significant impact on the matter. Whilst the legislation is silent as to the meaning of significant impact, the government has developed guidelines (http://www.environment.gov.au/epbc/publications/nes-guidelines.html), to help proponents decide if this is the sort of action that needs to be referred to the Minister for assessment and approval.
Commonwealth approval is required for any action that takes place on Commonwealth land, or that is likely to affect Commonwealth land, if it has a significant impact on the environment. This extends beyond the nine matters of national environmental significance already mentioned to include all environmental impacts.
There are some actions that may be exempt from the Commonwealth assessment and approval requirements, even if they do have a significant impact. One exception is the logging of forests in areas that are covered by a Regional Forest Agreement (RFA).