Difference between 32 bit and 64 bit OS?

The difference is in the interaction with the CPU. 

Here's the simplified technical side to it. 
32-bit (also known as x86) and 64-bit (also known as x64) designate the width of the CPU register. The CPU register is a small amount of storage on the CPU, which the CPU uses to keep the data it needs for optimum performance. Today's CPU's are commonly 64-bit units that are backwards compatible with 32-bit. 

32-bit operating systems only make use of 32-bits of space on the CPU, and are only able to handle 2^32 addresses or 4,294,967,296 bits thus the 4GB of RAM limitation (Only 3.25GB will be usable.) 

64-bit operating systems make use of all 64-bits of space on the CPU, and are able to handle 2^64 addresses or 64-bit is 2^64 = 1.8446744e+19 bits, which is virtually unlimited RAM (at today's standards) 

Here's what it means for Windows 
1. Your computer can use a lot more RAM (over 17-billion GB's of RAM). Realistically, though Windows License limits Home Edition versions of Windows, to 16GB. Professional, Ultimate, and Enterprise editions can support up to 192GB of RAM. 
2. You'll see increased efficiency. Since Windows can access all that RAM, and due to how Windows 64bit allocates memory, less of your memory will be used by secondary systems, and overall higher efficiency. 
3. 32-bit technology only allows Windows to assign 2GB of RAM per application. With 64-bit allows up to 8TB, although Windows Licenses don't allow it to get that high due to their RAM limitations. This means that applications that are designed for use with 64-bit can make use off all the processing power and memory afforded to them. (You can do more without sacrificing power.) 
4. Windows 64-bit offers additional protections not available to 32-bit users. These protections include hardware D.E.P. (Data Execution Prevention), as well as Kernel Patch Protection, that protect you against kernel exploits, and require device drivers to be digitally signed which cuts down on the incident of driver-related infections.

What is the difference between a 32-bit and 64-bit CPU?

The two main categories of processors are 32-bit and 64-bit. The type of processor a computer has not only affects it's overall performance, but it can also dictate what type of software it uses.

32-bit processor

The 32-bit processor was the primary processor used in all computers until the early1990s. Intel Pentium processors and early AMD processors were 32-bit processors. The Operating System and software on a computer with a 32-bit processor is also 32-bit based, in that they work with data units that are 32 bits wide. Windows 95, 98, and XP are all 32-bit operating systems that were common on computers with 32-bit processors.

Note: A computer with a 32-bit processor cannot have a 64-bit version of an operating system installed. It can only have a 32-bit version of an operating system installed.

64-bit processor

The 64-bit computer has been around since 1961 when IBM created the IBM 7030 Stretch supercomputer. However, it was not put into use in home computers until the early 2000s. Microsoft released a 64-bit version of Windows XP to be used on computers with a 64-bit processor. Windows Vista, Windows 7, and Windows 8 also come in 64-bit versions. Other software has been developed that is designed to run on a 64-bit computer, which are 64-bit based as well, in that they work with data units that are 64 bits wide.

Note: A computer with a 64-bit processor can have a 64-bit or 32-bit version of an operating system installed. However, with a 32-bit operating system, the 64-bit processor would not run at its full capability.

Note: On a computer with a 64-bit processor, you cannot run a 16-bit legacyprogram. Many 32-bit programs will work with a 64-bit processor and operating system, but some older 32-bit programs may not function properly, or at all, due to limited or no compatibility.

Differences between a 32-bit and 64-bit CPU

A big difference between 32-bit processors and 64-bit processors is the number of calculations per second they can perform, which affects the speed at which they can complete tasks. 64-bit processors can come in dual core, quad core, six core, and eight core versions for home computing. Multiple cores allow for an increased number of calculations per second that can be performed, which can increase the processing power and help make a computer run faster. Software programs that require many calculations to function smoothly can operate faster and more efficiently on the multi-core 64-bit processors, for the most part.

Another big difference between 32-bit processors and 64-bit processors is the maximum amount of memory (RAM) that is supported. 32-bit computers support a maximum of 3-4GB of memory, whereas a 64-bit computer can support memory amounts over 4 GB. This is important for software programs that are used for graphical design, engineering design or video editing, where many calculations are performed to render images, drawings, and video footage.

One thing to note is that 3D graphic programs and games do not benefit much, if at all, from switching to a 64-bit computer, unless the program is a 64-bit program. A 32-bit processor is adequate for any program written for a 32-bit processor. In the case of computer games, you'll get a lot more performance by upgrading the video card instead of getting a 64-bit processor.

In the end, 64-bit processors are becoming more and more commonplace in home computers. Most manufacturers build computers with 64-bit processors due to cheaper prices and because more users are now using 64-bit operating systems and programs. Computer parts retailers are offering fewer and fewer 32-bit processors and soon may not offer any at all.

 64 bit is always better OS than 32 bit in terms of speed. In simple ways the time taken by a 64 bit OS to transfer data between processor and RAM will be half than time taken by 32 bit. 

Maximum RAM that your OS can 
support : 
Windows 8 64 bit Enterprise,Prof 
essional : 512 GB 
Windows 8 64 bit :128 GB 
Windows 8 32 bit : 4 GB 
Windows 7 64 bit Ultimate, Enterprise 
& Professional :192 GB Windows 7 64 
bit Home Premium:16 GB 
Windows 7 64 bit Home Basic : 8 GB 
Windows 7 32 bit (all editions except 
Starter) :4 GB 
Windows 7 32 bit Starter : 2 GB 
Windows Vista 64 bit Ultimate, 
Enterprise & Business: 128 GB 
Windows Vista 64 bit Home 
Premium :16GB 
Windows Vista 64 bit Home Basic : 
8GB 
Windows Vista 32 bit (all editions 
except Starter) : 4 GB 
Windows 7 32 bit Starter :1 GB 
Windows XP 64 bit : 128 GB 
Windows XP 32 bit : 4 GB 
Mac OS X 64 bit :96 GB 
Linux 64 bit :1 TB 
Linux 32 bit :4 GB 
Linux 32 bit (with PAE) :64 GB