Second-order thinking is too abstract: some time thing which is obvious for you might not be for other e.g. binary search is not always a good option, it can be obvious to you (here you are an intelligent person with acquired knowledge) and for novice to this concept; their second order thinking would be to find out what Binary Search is and then why not it is always good to use it.
I think second order is trying to convey to look beyond what you have good in your first glimpse and try to connect dots. I haven't done much study on it but that what I get from it.