Linus, from Tech Quickie, explains the difference between 32 and 64 bit computers. Long store short: it all boils down to how much RAM memory a processor can handle. You need to remember that all parts in a computer need to fit in the ranges they should: a processor will determine what type of RAM memory you can use, for example and a motherboard will determine what type and version of processor you need to use.
For example, a 32 bit processor can handle up to 4 GB of RAM (2^32 bits), while a 64 Bit processor can handle up to 16 billion GB of RAM(2^64 bits) or this much RAM: 18.446.744.073.709.551.616 bits or 17.179.869.184 GB. Wow, that is a lot.
That does not mean that you can put that amount of RAM into your computer as the motherboards and type of RAM can set a limit. Older motherboards can’t go beyond 4 GB of RAM, newer ones may go up to 64GB of RAM. DDR3 is also twice as slow as DDR4.
In any case, that is the difference between 32 and 64 bit processors or computers.
But was is a software driver? It is a piece of data collected in one or more files (usually an .inf file among them) that instructs the computer on how to work with a given device: