The stated aim is actually stated explicitly in the Section 1. Policy. part of the order.
(a) It is in the national interest to promote clean and safe development of our Nation's vast energy resources, while at the same time avoiding regulatory burdens that unnecessarily encumber energy production, constrain economic growth, and prevent job creation. Moreover, the prudent development of these natural resources is essential to ensuring the Nation's geopolitical security.
As such, the main goals are:
Increase domestic energy production and thus supply; which was intentionally decreased by Obama administration policy aimed at reducing carbon energy sources.
Increase economic growth via the means of cheaper energy (due to increased supply)
Increase job creation (both directly in carbon energy sector, e.g. coal/oil; and indirectly by improving the economy by having cheaper energy)
Ensure geopolitical security (which basically means reduce dependence on imported energy sources; especially in light of the fact that majority of those sources are in hostile-lish or volatile nations - Middle East, Venezuela, Russia).
(b) It is further in the national interest to ensure that the Nation's electricity is affordable, reliable, safe, secure, and clean, and that it can be produced from coal, natural gas, nuclear material, flowing water, and other domestic sources, including renewable sources.
This is basically the official GOP energy policy (at some point labeled "all of the above").
(c) Accordingly, it is the policy of the United States that executive departments and agencies (agencies) immediately review existing regulations that potentially burden the development or use of domestically produced energy resources and appropriately suspend, revise, or rescind those that unduly burden the development of domestic energy resources beyond the degree necessary to protect the public interest or otherwise comply with the law.
This is just elaboration on the very first bullet point - the goal is to reduce regulatory burden that artificially (intentionally) curtails domestic energy supply on the carbon side.
(d) It further is the policy of the United States that, to the extent permitted by law, all agencies should take appropriate actions to promote clean air and clean water for the American people, while also respecting the proper roles of the Congress and the States concerning these matters in our constitutional republic.
This is basically rolling back Obama administration's political attitude/philosophy of increased Executive power that runs around legislative one. Kinda ironic, coming out of "authoritarian"-accused Trump, but that is the mood/philosophy/politics of much his base (double extra ironic since the tactics chosen is Executive action :).