What do you mean by 32-bit and 64-bit machine?

As far as I understand it is the length of memory addresses, integers etc.
So if my computer is 32-bit integer can have maximum value of 4,294,967,295 which is the maximum 32bits can store right?

But I have heard a lot about games which require 4gb ram(which is 32bits) but will also run on 2gb ram. Whats going on here?

Also why instruction set architecture changes as we move to 64-bit system.(x86-32 to x86-64)?

The bits is how large of a chunk a processor can process at a time. So a 32 bit processor takes 32bit input and 32 bit output.

The major reason for the upgrade to 64 bit processing was due to the memory restraints of 32 bit processors. A 32 bit processor in theory can only allow up to 4gb in data pointers meaning that you can not exceed 4gb of ram on a 32bit system. Where 64bit in theory can handle 192gb of ram.

And as far as architecture both use the X86 command set just 32 bit or 64bit variants of such. Where a X86-64 can also process X86-32 applications