An arcball is a way of making a 3d object interactive, by mapping 2d input coordinates into a 3d vector.
About Arcball
An arcball is an interface for manipulating a 3D world in an intuitive way, and can be thought of as a virtual trackball. This snippet presents a simple arcball library which automatically attaches itself to your sketch and allows you to freely rotate the world in 3D dimensions about a specified point. Extensions to this library might change the way the mouse movements are interpreted, add a zoom control, and so on. This arcball library is adapted from code by Simon Greenwold for Yale's Model Based Design class. The arcball method of interaction was introduced by Ken Shoemake in his 1985 SIGGRAPH paper "Animating rotations with quaternion curves".
More information and examples: http://wiki.processing.org/w/Arcball