A core, in the archaeological sense, is the basic raw material building block for a stone tool. A flint knapper seeks out the most appropriate raw material available for the job. If the resulting tool is to be a projectile point or intricate tool the quality of the stone might be very good indeed,imported from many miles or hundreds of miles away.
For an expedient tool--a tool that needs to be used right away and then may be left behind--the raw material may be whatever is most available. The ability to identify where a particular raw material comes from is thus a very interesting quality of a core or tool manufacturing site.