system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: the difference between 32-bit and 64-bit Windows installations, and their relation to the hardware.
gpt
Think of a computer like a great library. There are all kinds of books (storage) but also a librarian who helps figure out what books you need. The librarian has 32 assistants who help fetch books on bicycles and bring them back to the librarian. If someone comes in wanting all the books on dinosaurs, and there are 65 of such books, the books will all get there in three trips. The first trip all the assistants go out and get the books on, then go back and on the second trip they all get another book and on the third trip only one has to go and get data, but it still takes just as long, since the important thing is how long a trip takes. 

So to get the books it requires three bicycle trips (but we can just call them cycles, so three cycles). However, if the librarian had 64 assistants, it would only take two cycles. There would be a dramatic speed boost, but NOT double, since there would still be on trip that only one assistant was needed, while the others are there but unable to make it go faster. 

If there were 256 books on dinosaurs, then with 32 assistants it would take 8 cycles but with 64 it would only take 4. However, if there were only 20 books on dinosaurs it would make no difference if there were 32 assistants, 64 or even 128! It would still just be one cycle. 

A computer works in much the same way. The computer fetches data from memory, but can only fetch so much at one time. If the computer is running at 64 bits, it can fetch 64 bits of data (and work on it) during one clock cycle. A computer running at 32 bits can only handle 32 bits of data during a clock cycle. 

Well, now imagine that there were 64 assistants, but the librarian didn't know where half of them were! The librarian could only use 32 at a time, even though there were twice as many available. A 32 bit version of windows only knows how to "find" bits worth of data at a time, even though your 64 bit computer has other resources waiting that cannot be used. The 64 bit version of windows doesn't change the hardware any (of course) but it helps the hardware FIND all those assistants. 

EDIT: And although this wasn't asked for, a dual core processor is like having two librarians, and the "speed" in gigahertz is how fast the bicycles can go. (Or more specifically, how long it takes them to make the trip. A 1 Ghz bicycle can make one billion trips in one second.)