A 64-bit processor is one which handles (or can handle) 64 bits of data in a single operation (for example addition of two registers each containing 64-bit integers, or accessing a memory location via a 64-bit pointer).
A 64-bit operating system is one which is compiled to take advantage of the 64-bit instructions provided by a 64-bit processor and as such will not work on a processor that does not support these instructions. One advantage of 64-bit Windows for example is that it can take advantage of more physical RAM than the 32-bit version of Windows.
Many mainstream 64-bit processors also have 32-bit instructions so that they are able to run either a 32-bit or a 64-bit operating system.
See 32-bit vs. 64-bit systems.
– Mehper C. Palavuzlar – 2010-10-10T08:49:24.257You are getting someone who saw a "64-bit" sticker on the box the computer came in. – Daniel R Hicks – 2012-06-27T15:44:58.540