In layman's terms, as I (a layman) understand it: it means more current/capacitance. For music it means the amp has the resources to react quickly and fully to musical peaks that require more power. In listening terms, it means that the amp has better dynamics (micro and macro) and generally a higher capacitance amp will have more of an easy and flowing sense to the sound b/c of the more than adequate capacitance.
60,000 is already more than most amps. 120,000 is more than about 99% of amps, I think. Will you be able to hear the difference? Probably, but hard to tell. Depends on how hard your speakers are to drive and how loud you listen.
I have 2 amps, one rated at 300WPC 8 Ohms with 28000 Auf and the other rated at 85 WPC at 8 Ohms with 88,000 Auf. My speakers aren't hard to drive (rated at 91db and 8 ohms) but the amp with "less power" but more capacitance seems subjectively louder and definitely plays peaks like crescendos, cymbal hits, or drum hits better and more easily and sounds more realistic than the higher powered amp. That's why a lot of "low power" but high current amps can often do a surprisingly good job driving speakers. You rarely need all the power your amp can put out, but you often need high current delivery, even if only for a brief time.
