Your CPU or processor is the heart of your new computer, it is the main chip which carries out all instructions and calculations needed to run your programs.
Generally speaking the faster a processor runs the faster it can carry out instructions so all other things being equal a faster speed (GHz) means a faster computer.
Some processors have a Turbo speed which they can run at for short bursts of extra processing power when required, we list CPU's by base speed and include Turbo speeds if a chip is capable of it.
Cores are the number of instructions a CPU can process at the same time, a quad core CPU can carry out four different instructions simultaneously, often a quad core CPU running at a lower speed than a dual core processor can end up outperforming it in many tasks, this is highly software dependent though.
There is also a technology called HyperThreading which further optimises CPU Core performance and offers the operating system double the number processing threads to use over a none HyperThreaded chip, this can enhance multi-tasking performance further in some workloads. If a CPU has HyperThreading we display (HT) in the description.
Intel's latest mainstream CPUs are the 9th Generation Coffee Lake (Refresh) chips. You can work out which generation a processor is from as the first number in it's designation is the generation.
An i7 8700K is an 8th generation chip, the i5 9600K is a 9th generation chip.