Optical digital audio cable for Apple TV
You can use this cable to connect your Airport Express to your home stereo (or theater) receiver if your receiver has an optical (AKA Toslink) digital input.
Apple Support has a How-To article about it, search for "How to set up and configure AirPort Express for AirPlay and iTunes"
The 3.5 mm output on the Airport Express is both analog and mini-Toslink optical, just like on a Mac.
The Airport Express has an internal Digital to Analog Converter (DAC) which provides the signal for the analog output. Experts report that the internal DAC sounds good, especially in early versions of the Express. My experience agrees with this. The DAC is however limited to CD quality output (16-bit PCM encoding at 44.1 kHz sampling rate) which means if you send it a higher resolution encoding it will be down sampled to 16-bit/44.1 kHz.
Whether to use the analog or digital connection to your receiver also depends on the quality of the DAC in your receiver (it has a DAC if it has any digital inputs).
When you use the optical cable to connect the Express to either a receiver or an external DAC+amplifier you bypass the Express' internal DAC and the external DAC receives the unconverted digital signal. If the receiver's DAC or external DAC is of higher quality/capability than the internal Express DAC you may be able to hear the difference. You can experiment with both the analog and digital out from Express to receiver to see which you prefer.