Quicksilver can do lots of different things. At the most basic level you can use it to launch applications, and it’s much faster than using the mouse or using Spotlight for that purpose. But there are other application launchers that do the same thing—Quicksilver’s advantage is that there are lots of plugins for it that let you do other tasks. For example, you can use Quicksilver to compose and send an email with an attachment.
I tended to use Quicksilver mostly as an application launcher, and it’s not necessarily better than Butler or Launchbar for that purpose. And there’s a steep learning curve to Quicksilver, but if you’re committed to learning it you will find that it’s extremely powerful and can make simple tasks faster.
If you want to see what it can do, google quicksilver tutorial and you can see some videos that can guide you through setting up plugins and performing basic actions.
@Bri L: I think if you’re a power user, Quicksilver is more powerful. But that’s just what I’ve heard as the general consensus. I stopped using Quicksilver when it stopped being developed—I don’t want to invest time in learning how to use a dead program.