for charts to see, visually, how parts like GPUs and CPUs stack up next to others, you can look up benchmarks -- passmark.com has user-submitted benchmarks that show an average of performance, so you can see what's better than what. they aren't the be-all end-all, but when you're just learning, it can be extremely helpful to have a list of nearly every processor and graphics card sorted from best to worst. when friends and relatives are looking to buy computers, i always point them towards benchmarks, since 8 or 16GB RAM or a 3TB harddrive are easy specs to understand in a product listing ("bigger is better" usually!), but only professionals or enthusiasts will know right off the bat how a GTX 960M will perform.

for your specific examples:

"quad core" (you will also see duocore, hex-core, octa-core, etc) refers to the number of cores a processor has. think of each core as being like a person in a group project. ideally, work should get distributed evenly among these people, and the more people working, the faster the task is completed. (unfortunately, sometimes programs will not properly utilize all of these cores, which is the equivalent of all the work getting dumped on one person while everyone else in the group fucks off until the grade comes in. that's why processor speed is also important!)

i3, i5, and i7 refer to tiers of intel processors in a given generation - i3 processors tend to be the least powerful, while i5 is middle of the pack, and i7 will be the best offered. when looking at intel processor models, they'll usually be 4 numbers (and sometimes a letter), where the first number indicates generation. things can get terribly confusing from there (some of the high end CPUs in an older generation can be better than the mid end CPUs in a newer generation, for example, or occasionally they will add letters that indicate a particular function, like "K" for easier overclocking) - which is where benchmark charts come in handy!

processors (CPUs) are the thinky parts. like the student example above, they're what handle the workload: when a computer is told to do something, the processor is what deals with most of the stuff that goes into actually getting it done.

a GPU (graphics processing unit) handles what happens visually--the big focus here for most people is on making things look pretty in gaming, but plenty of stuff leans on the GPU, such as rendering. graphics cards are larger, standalone units that slot into the motherboard, and provide superior power because they're dedicated solely to the task of handling visual stuff; integrated GPUs come with another piece of hardware (usually the CPU) and are less capable of handling the same tasks as a dedicated GPU because it siphons off other resources. integrated graphics are most common in non-gaming consumer products, like laptops, tablets, etc.