A commitment to deliver (a service, funding, an item) that is subsequently set aside. The broken promise is then explained with the glib expression "oh, but that promise was non-core".
Now generalised to non-political situations, too.
Origin: Australian federal elections at the turn of the 20th/21st centuries. The conservative party (known as the Liberal/National coalition) made a number of election promises which were broken soon after the election. The prime minister, John Howard, attempted to explain this behaviour by claiming that some promises are "core" and some are "non-core" and thus, don't count.
Not only did "No tax increases, no new taxes" turn out to be a non-core promise, but in the campaign, Howard had also given a solemn undertaking that "I'm not going to break any promises". That one was certainly non-core.
Laurie Oakes (Australian political reporter/writer)
Excerpt from National Nine News (network TV) 12 May 2005
as quoted at news.ninemsn.com.au