The technological terms 64-bit and 32-bit basically refer to the manner in which the central processing unit of a computer handles information on the computer. The 64-bit capable CPUs coupled with 64-bit operating systems are able to handle larger chunks of information and more efficiently than a 32-bit systems. Also 32-bit systems can not utilise more than 3GB of system ram which limits the performance of computers with more than 3GB of RAMs installed. 64-bit on the other hand can accommodate more than 3GB of RAM,hence, the 64-bit system is more efficient and responsive when running multiple tasks.
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The 32-bit Intel CPUs could access more than 3GB of physical memory. The address space of any individual process or "segment" was limited to 4GB because the pointers were 32 bits long. But the Intel page table allowed physical addresses larger than that. See https://en.wikipedia.org/wiki/Physical_Address_Extension