Both are digital outputs for audio. SPDIF is generally used for home/consumer use and Firewire (1394) is more common in pro applications although USB 3 is taking over for that.

In a home theater/stereo pretty much all modern amps and receivers have a SPDIF capable input. If you want to hook your computer up to a good pair of hifi speakers of the type you'd find in a home theater system that's the way to do it but if you're using a 10 - 50 dollar (ish) pair of desk top speakers and are happy with that then there's no reason to think about digital output.