Can someone explain the advantage of faster cadence to me?
Fairly complicated to explain simply - but I'll have a go! Generally speaking, faster cadences (90+) place less mechanical strain on your leg muscles, whereas lower cadences are more ecomonical (in terms of oxygen cost, VO2). That being the case, there is an argument that a true optimal cadence does not exist. From a practical point of view (according to Burke's book), optimising cadence is of value only when your power output exceeds 200W - less than that amount, cadence may not in fact change anything.
The choice appears to be a trade-off between: 1. Less muscle stress and better blood flow with a higher demand on your metabolic system (higher cadences) & 2. More muscle stress but less demand on your metabolic system (lower cadences).
A really good reference is Chapter 4: High-Tech Cycling - Edmund R. Burke (Editor). Specifically the chapter by Lucia et al. titled "Optimizing the Crank Cycle and Pedaling Cadence".
Burke's book looked at data from professional races (Giro, Tour & Veulta) and concluded that mean cadence during mountain ascents was ~70 and ~90 during time trials and flat stages. This, however, was variable and he gave the examples of Armstrong pedaling around ~100rpm (39x23) and Riijs ~70 rpm (53-tooth) in respective climbs during the Tour.
To sum up: pedal fast - your legs will last longer but you will be sucking in the breaths, pedal slow and you will place more demand on your legs and less on your breathing.
I pedal around 90-100. Hope this was of some help!