Do you understand the definitions of the words, 'core', and 'principle'?
In a nutshell, the phrase conveys the concept of deeply held, fundamental convictions, that a person possesses. Normally, such convictions are forged within a person at a very young age.
As times change, and societal events move and shake our world, most people are guided in their thinking and actions by their core principles. This type of person doesn't 'evolve' or 'transform' over time, in reaction to what's happening around them. If asked how they think about anything, they can always give you a straight, unambiguous answer, because their opinions are guided by something much deeper than surface level thinking.
Of course, there's also the type of person who's compromised their core principles so often in life, that they're continually having to formulate what they think is the proper, or winning stance, on every single issue they face in life. That type of person never has a ready answer to any question you present to them, because they've betrayed whatever core values they once possessed. This is the type that changes their views to fit a perceived 'winning' or popular stance.
This is what I observe to be the fundamental difference between Ted Cruz and Scott Walker.
With all due respect to Cruz, he has never had to run an entire state. He is a lawyer and they specialize in arguing. And, further, they are as elastic as a person can be. So, I may prefer a person who is slogging it out in the trenches, dealing with unions and liberals and other crazies over a person who can pontificate. And, BTW, Cruz said he would do away with the IRS which is an absolute, utter boneheaded thing to say. He would just have to create a New Tax Collection Dept., the TCD and START ALL OVER no matter what tax system we had. But, if Cruz and Walker were on the ticket, I would still vote for them.