The new audio chip is an incremental update of the original Sound Processing Unit (SPU) called... SPU2! Improvements include 2 MB of internal memory and 48 audio channels, twice the number available on the original SPU.
The SPU2 consists of two internal sound processors, referred to as CORE0 and CORE1, and runs at ~36.86 MHz. Each processor handles 24 channels.
Curiously enough, these are still two independent controllers, and configuring them requires altering their respective registers. However, Sony warned developers that both sets of registers must be updated at least 1/48000 seconds apart. If you hurry too much, the behaviour of the SPU2 becomes unpredictable.
The SPU2 inherits the same effects available on the original SPU. The provided memory serves as a 'work area': raw waveform data can be stored there, while additional space can be allocated for processing and applying effects.
Finally, the chip can mix all channels into stereo output. Now, here is the interesting part: the SPU2 can feed the mixed stereo sample back into itself as a new input. This allows the EE to access it (to mix it with additional audio, for instance), or apply further effects, such as reverb, echo, and delay.

Video - Kingdom Hearts II (2005). Without reverb.

Video - Kingdom Hearts II (2005). With reverb.
Audio out
The audio signal is outputted through two interfaces:
- Digital Audio: Referred to as the Sony/Philips Digital Interface or 'S/PDIF', it's a digital signal that inherently carries less interference.
- Analogue Audio: Passes through the digital-to-analogue converter before reaching the AV Multi Out port. Most TVs are compatible with it.