64-bit and 32-bit refer to how addresses and memory are handled in different instruction set architectures. For clarity, the terms ‘32-bit’ and ‘64-bit’ have dual meanings. The first refers to the size of addressable chunks of memory. Memory is organized in chunks, called words, that a processor can handle at once. 32 and 64-bit systems respectively handle chunks of memory that are 32 and 64 bits in size. The second meaning refers to the size of the addresses used to catalog all of the addressable points in memory. In other words, each word in memory has an address that the processor uses to find it. 32-bit systems use 32-bit-long addresses, and the same follows for 64-bit ones. Note that it just so happens that these systems have the same address size and word size. It’s not necessarily the case. For instance, early PCs often had 8-bit words and 16-bit addresses.

Most commercially available systems today come with 64-bit capable processors and pre-installed 64-bit operating systems. 32-bit applications are compatible with them because the 64-bit format is backwards-compatible. The space addressable by 32 bits is a subset of what is addressed with 64, and the processors are built to handle 32-bit chunks of memory. Simply put, if you have a 64-bit compatible processor, run 64-bit software.

One extra consideration is the operating system. Applications other than drivers and similar software interface with the hardware through the operating system. Therefore, it is important to consider the type of operating system installed. 32-bit OSes can only handle 32-bit operations, but 64-bit ones can properly use both.

Altogether, none of this is likely to be an issue with machines from the past few years. Lately, AMD and Intel have introduced different brand names and code names for their processors, which can get confusing quite easily. In case you’re running older hardware, here’s a list of a few 64-bit capable processors.

AMD (aka "x86-64", "AMD64", or "x64")
Athlon 64
AMD Athlon 64 X2
AMD Athlon 64 FX
AMD Athlon II (X2/X3/X4)
AMD Opteron
AMD Turion 64
AMD Turion 64 X2
AMD Sempron ("Palermo" E6 stepping and all "Manila" models)
AMD Phenom (X2/X3/X4)
AMD Phenom II (X2/X3/X4)
Intel (aka "IA-32e", "EM64T", or "Intel 64"
Netburst family
some Celeron D's: LGA 775 "Prescott" models
some Pentium 4's: "Prescott 2M," "Irwindale" "Cedar Mill"
Pentium D
Pentium Extreme Edition
Intel Core
Xeon: Core 2, Dual Core, Celeron
Nehalem: Core i3, i5, i7, Intel Atom