Emulation requires the creation of a computer in software. This includes a CPU, memory and all the ancillary hardware necessary to make a computer that is as close to actual hardware as possible.
Every CPU instruction is examined and converted to the language used by the emulated CPU prior to being run on the host CPU. It is not the same as running code directly on the host CPU because the CPU is a software construct that is fully isolated from the host CPU.
That isolation makes it suitable for the emulated computer to be moved to any other system, even with an entirely different CPU type, because it is independent from the host CPU and depends only on the emulation software. The host CPU and the emulated machines can have wildly different CPUs.
This isn't "just" a 64-bit machine acting as a 32-bit machine, it is a 64-bit machine running an entire CPU in software on top of a real CPU.
The alternative to emulation is virtualisation. In virtualisation the software emulates only hardware and related interfaces around the CPU and not the CPU itself. Code is run directly on the host CPU resulting in near native speeds at the cost of requiring the same CPU architecture in the host and guest machine.
1This makes no sense, as all the processors through the Pentium 4 *ARE* 32 bit. What emulation are you talking about *exactly?* – Keltari – 2019-10-15T03:20:25.157