Hello to all,
While it is technically correct to say "it has to do with the maximum addressable memory", the true definition of 64-bit computing refers to the CPU's ability to process instructions and data 64-bits at a time.
Fair warning: this subject is worthy of college-level computer science courses, but I hope to keep it simple by offering a few examples from PC history.
The original IBM Personal Computer was built using an Intel 8088 CPU. It was able to process instructions and data 16 bits at a time. However, for compatibility reasons, Intel chose to design it with an 8-bit data bus (used for communication with peripherals). It also had a 20-bit memory bus, which allowed it to support up to 1MB of RAM. Was it a 16-bit, 8-bit, or 20-bit processor? Answer: it was a 16-bit processor.
The second generation of IBM PC's, called the IBM PC AT, included an Intel 80286 processor. This processor could process instructions 16 bits at a time. It also had a 24-bit bus, which allowed it to support 16MB of RAM. This processor was, technically, also a 16-bit processor.
The third generation of Intel x86 processors was the 80386, which was Intel's first 32-bit architecture, owing to its ability to process instructions and data 32 bits at a time. It initially came in two versions, one for consumer PC's and the other for 'high-end' systems. The 80386SX had a 24-bit memory bus, so it supported up to 16MB of RAM. The 80386DX had a full 32-bit memory bus, and so it supported up to 4GB or RAM. The point is that both the 386SX and the 386DX were adequately referred-to as 32-bit processors.
Back in 1986 (when the i386 was released) 16MB of RAM were more than Windows could use. In fact, it was physically impossible to fit 16MB of RAM on a PC motherboard, even with a 32-bit processor on board. I was in college during those years, and I remember thinking about the 32-bit addressing capability (4GB of RAM) much in the way one might think today about a manned trip to Mars, or setting up a permanent station on the moon. Possible? Maybe 20 years from now...?? If we're lucky?
Fast forward to the year 2007... It's been 21 years since the first 32-bit CPU for the PC was released, and we are ~almost~ at the point where 4GB of RAM is affordable for the masses.
Should Plue worry about having a 64-bit PC? Probably not. But if Plue insisted on having a system that will run today's 32-bit Windows and still be able to support 64-bit applications in the future, there are two basic choices. AMD64 and Intel Core. Both come in single- or multi- core models. I personally recommend the AMD64's, but that's just personal preference. 1GB is probably enough RAM for Plue today, but to help ensure compatibility with future 64-bit applications, Plue should make sure the computer is upgradable to 4GB or even 8GB or RAM.
I hope I didn't make this topic too confusing. By the way, I agree 100% with Kees' statement that "For people like you and me, 32 is quite is OK. It will run everything you need."