Anyone using a computer spends a lot of time locating files and applications and carrying out actions on those items. The Finder is a reasonably good tool for getting a visual overview of the contents of your disk, but it isn't ideal for quickly locating and manipulating files, especially if you have a deep and complicated folder structure, or if you prefer keyboard navigation to using the mouse.
Quicksilver allows you to find what you need quickly and easily, while keeping your hands on the keyboard. For example, if you want to launch an application hidden in the depths of your file system, simply activate Quicksilver with a keystroke, type a few letters of the application's name, then hit Return or Enter to launch it. When you don't need Quicksilver, it keeps out of your way, preserving precious screen real estate, yet you can summon it instantly with a keystroke.