Exactly what is a 64-bit processor?

[Callum]

A slightly more understandable version might be that 64-bit processors allow the processor to process twice as much information at a time. 64 bits (binary digits - 1s or 0s). A 32-bit processor can only process 32 bits at a time, and if it needs to process a 64 bit thread, it must process it in two halves.

A dual-core actually has two processor cores, and so can work on twice as much different information at a time. While a 64-bit processor and a 32-bit dual-core processor can technically process the same amount of information at a time, the 64-bit thread in the single core will be one item of information. In the dual-core, the two threads could be completely unrelated (one thread from Windows Media Player, and one from Baldur's Gate, for example). The 64-bit processor is also limited by the fact that not all threads are 64-bit. If a 32-bit thread is sent to a 64-bit processor, the processor works at half of its efficiency.

However, you can get 64-bit dual core processors as well, which are clearly superior no matter which way you look at it (For example, the AMD Athlon 64 X2 range).