An example of a casted ability is Mortar Volley for the Trooper (Death from Above for the Bounty Hunter). Without any Alacrity, that move takes 3 seconds to complete. With 5% Alacrity, it will take 2.857 seconds (3 / (1 + 0.05)).
Since the 3.0 patch, Alacrity affects virtually everything: Cooldowns (internal timers, the Global Cooldown (GCD), and ability cooldowns), cast and channel times, tick speed of channels and Damage over Time (DoT) abilities, etc. As such, 1% Alacrity is essentially a 1% increase in Damage or Heals Done per Second (DPS/HPS). This is a bit simplified, since using Alacrity means giving up other stats you could use instead, but overall Alacrity is now very useful.
