the "core" is the part with all the fins on it that actually does the cooling. when it says it has a 3 core, for example, it means there are 3 rows of cooling tubes going across(or down, depending how it is set up)the radiator. more "cores" genarally means more cooling capacity. it is easy to figure out how many "cores" a radiator has. just take off the cap and count how many tubes make up the thickness of the radiator, front to rear.2 cores seems to be the norm, with 3 and 4 cores in "heavy duty" applications, like trucks or hi perf cars or cars with air conditioning.