What is the difference between SQL Server 32-bit and SQL Server 64-bit application and how do you know whether a computer is 32-bit or 64-bit?

64 bit computers process data in larger chunks than 32 bit computers. This means a number of things, but the big 2 are:

1) When programs are written to support 64-bit processors, those programs will generally perform faster than on a 32-bit processor of the same speed. This is partially because 32-bit computers must handle 64-bit numbers in two steps, whereas 64-bit computers only need to use one step.

2) 64-bit processors can address more memory than 32-bit processors. This means your server can have more RAM, and therefore can store more data in memory, making memory-intensive programs like databases faster.