system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What is the difference between Windows Operating systems 32-bit and 64-bit? Why do they exist and what are they used for?

I came across some of my old childhood games like Heros of might and magic 2 and Dark Reign 2. I tried installing them on my Acer Aspire 5532 Win 7 Ultimate 64-bit, and I wasn't able to due to compatibility issues. A technical explanation coupled with a ELI5 answer would be awesome

Edit: Addition: How about x86 vs x64?
gpt
The difference in 32 bit and 64 bit is the size of the number your cpu can work on. A 32 bit processor can work on numbers up to 32 bits in length (for example an unsigned 32 bit integer can hold any value from 0 to 4294967295 ) and a 64 bit processor can work with numbers up to 64 bits in length ( an unsigned 64 bit integer can hold any value from  18446744073709551615 ). The most major implication of this is that 32 bit processors can only address 4294967296 (computers start counting at zero) bytes of memory, which means that no 32 bit processor can use more then 4GB of ram. Since 64 bit computers can use much longer numbers, they can access much more ram. 

There are other, more arcane, befits of having the ability to use bigger numbers that programmers can use to their advantage, such as being able to shove two 32 bit numbers inside one 64 bit slot inside the processor so you don't have to fetch those two numbers from memory outside the processor.

The inability to run old software on your Win 7 doesn't stem from it being 64 bit, it stems from Microsoft ~~now handling 32 bit executables in a manner much different from how they did when most computers were 32 bit.~~ removing window's ability to work with 16 bit executables.