The above topic i.e. what exactly is 32 Bit and 64 Bit Processor, is very easy to explain and also most hard to understand. I have searched all over the web and have applied all my Engineering skills to understand this. The meaning lies within the question itself. The simple to explain is that a 32 Bit processor can process 32 Bits of data at a time and 64 Bit Processor can process 64 Bit of data at a time.
This means that the maximum processing data bits for a processor of 32 Bit genesis is 32 Bits of data at a time and for 64 Bits genesis it is 64 Bits of data at a time. Depending upon the ability of Processor from Hardware side the System Software or Operating System running on the Processor can be classified as 32 Bit or either 64 Bit OS. Like Windows 10 32Bit/64Bit versions or Ubuntu Linux 32Bit/64Bit versions.
Going further deep every processor has inbuilt registers like scratchpad which stores data or results while CPU is busy processing any instructions. The size of these registers determine the type of processor i.e. 32 Bit or 64 Bit. It these registers can hold 32 Bits of data or results it is 32 Bit processor and if it can hold 64 Bit of data or results it is 64 Bit processor. These registers lies in between the CPU and the Cache Memory (Processors may have L1, L2 or even L3 level of Caches) of the processor, Cache memory pre-fetches all the data required for processing from the RAM in advance even before the Processor is busy completing any other instructions depending upon its sizes.
This helps CPU to reduce data or instruction fetch time from RAM modules which are relatively slower during access. Now when any instruction is being executed which requires data to be manipulated, CPU loads the data into its internal Registers depending upon its Processing capabilities i.e. either 32 Bit data or 64 Bit data from the Cache memory at a time.
Many things can be derived or can be differentiated in various view angles comparing in between the system running on 32 Bit and 64 Bit Processor. Like 64 Bit Processors can easily handle large complex applications like 3D modelling/processing or advance gaming applications requiring huge amount of calculation or HD media etc. For normal operation requirements like simple word-processing or media capabilities 32 Bit processor performs relatively better than or is similar with 64 Bit Processors, there is relatively no big difference.
Another there is one limitations in Hardware respect using 32 Bit/64 Bit Processors i.e. a 32 Bit Processor can recognize or is capable of accessing 4GB of RAM in max in comparison to 64 Bit Processors which can access much more that 4 GB RAM limitations.