Hii Basically, for engineering students ,placements can be categorized broadly in two ways either core or non-core. Here core means the companies visiting the campus(or off campus) for filling their positions related to the core engineering disciplines. 

For eg. If a mechanical engineering student goes for any automobile company or any manufacturing related company. Or any electrical engg. Student for some instrumentation or automation company can be considered of the core type job.

Otherwise there are companies that are not related to any of the core engineering discipline and takes the students for different profiles such as Business Analyst, operation manager, Marketing management, Data analyst. For them it doesn't matter a student is from any engg college or any other ,they only look for students good in aptitude, logical reasoning ,communication skills,good with numbers (data analyst), presentation skills etc. These type of companies can be considered as non core companies for engineering students.

Companies such as Mu Sigma, Affine analytics , Investment firms  such as Goldman Sachs etc.  Are some of them. They also provide a hefty pay package but then you have to work accordingly.

But this doesn't mean that core engg. Firms doesn't have job profile other than core. They also have management profile but for that they prefer MBA students. 

Also firms such as Goldman Sachs have core profile for computer engineering students as software engineers.

So it depends on the job profile that a company has to offer to the students. 

You cannot categorize a whole company as non core because it can be core for some ,as well as non core for others at the same time.

I think this clears your doubt regarding core and non- core.