From my limited understanding here is a basic overview:
XP (original situation):
DirectSound -> Hardware Abstraction Layer (HW accelerated) -> DirectSound3D -> EAX (Creative own extension to DS3D for advanced effects such as reverb)
Vista (era of workarounds):
Vista removes "Hardware Abstraction Layer". This makes games fail to load DirectSound3D and EAX as a consequence. So no 3D audio. Games will simply appear as if you do not have accelerator sound card in your system.
2 important software are created. OpenAL and Creative ALchemy.
OpenAL is cross-platform and open-source. Think of it like replacement for DirectSound3D. On Windows it still uses DirectSound as backend. All done in software (their vision of the future, which obviously makes sense).
Creative ALchemy restores DirectSound3D and EAX by intercepting DirectSound calls and translating anything necessary to OpenAL instead. This makes DirectSound3D/EAX kick back in with full HW acceleration support, basically resurrecting the missing hardware acceleration on Vista. It is not a 100% "clean" solution to the original problem, only a work around. So while ALchemy is very very good, it is not perfect. Or better said, ALchemy results are not 100% as original, as perfect or imperfect that may be.
These days 3D sound is done like this for example:
DirectSound -> OpenAL -> EFX (OpenAL own extension to OpenAL for advanced effects)