What is the CPU family in this case? And CPU cores meens the number of cores that a prossessor has, no?
It's probably more worth looking up the processor as tetsujin as done - in most cases, since that gives you a bunch of information about your processor.
Family 6 indicates it's a spiritual descendant of the Pentium Pro (AKA the P6) and core families (oddly enough, they've retained that all the way from pentium pro - the original P6 to modern processors - with the netburst family being family 15).
In a sense, it's the microarchitectural lineage of the processor. Considering the family has been around for roughly 20 years with a short break when intel went into the space heater business with the pentium 4, It's not exactly a handy piece of information to have.
Looking up that processor, it's a hex core processor with HT. Since your output shows one core - my guess would be it's a VM - so it's the number of cores allocated to the VM rather than the number of physical cores on the machine.
CPUID.family == 6 means it's anything from Pentium Pro (1995) to the latest Haswell (2014) except "Netburst" . For
CPUID.family == 6 you have to check the
CPUID.model field. You can find the ranges of model numbers by painstakingly trawling through all of the various specification updates while muttering obscenities under your breath (note: this is the traditional method). I don't know if there's a less insane way of deciphering it.