Hello,
I have some experience building computers so I should be able to help you out.
Computer hardware refers top the various component that go inside the case of the PC or laptop, they can be split into a few categories.
First you have a motherboard. This is a large series of chips which coordinate all the other bits of equipment in the computer. Everything goes through the motherboard, it's like a brain
The processor sits in the motherboard and it's usually a small square chip. This chip is one of the things the governs well your computer runs, how fast it is and how it copes with lots of different programs working at once. When you see an advert that says 'Intel Inside' that means the processer is made by Intel.
The graphics card is used for the visual side of your PC. It's most useful for running games, if that's your thing, or if you are a video editor. The more powerful your card the more intensive visual programs you can run. If you were looking to play blu-rays on your PC a good graphics card is necessary also.
Memory, like the processor help your PC run quicker and do more things efficiently. I you have higher level memory everything is smoother and faster. Memory is split in groups called DDR, he higher the number after the DDR, the better the memory.
Power supply is what keeps your PC powered. They plug into the wall of course, but making sure you have a strong enough power supply for all your other components is important. You can check what power supply is needed for what component when you buy them.
Its important to keep your PC cool and that's where fans come in. A lot of PC cases have them built in as do graphics cards, but it's a good idea to add some more to make sure nothing melts. You can higher grade fans for increased cooling or silent ones for quieter running. You can also get water cooling systems for extra efficiency and quiet.
Of course you need somewhere to store all your stuff and that's what a hard drive is for they come in memory measurements called Gigabytes, 1000 gigabytes is a terabyte which you see more and more these days. The bigger the better really, but get what you think you'll need. You can solid state drives now as well which are like hard drives practically, but work much quicker, so you access your files faster
You can add soundcards if you need to, but most graphics cards have them built in. If you want the best though you can add this in.
I hope this was helpful.