When the Z0 particle decays in the centre of the OPAL detector, it oftens decays into other particles which in turn decay yet again into more particles. In a typical physics analysis, one reconstructs this chain of events by extrapolating back the tracks of each of the particles as seen in the detector.
For instance, the Z0 will some 15% percent of the time decay into heavy mesons called B's. These fly away from the interaction point for a distance of up to a few millimeters before themselves decaying into a few lighter particles. The space point where the B decays can be reconstructed by tracing back the final particles paths to a point or vertex where they all meet. The distance between this point and the interaction point where the Z0 (which is at rest when created in OPAL) and the B are created gives a measure of the B meson's lifetime. Longer lived particles will tend to fly further away before decaying. Precision measurements of particles' lifetimes are greatly aided by being able to precisely place the point where the heavy particles decay.
The Silicon microvertex detector serves to pin down exact geometric information about where the various particles come from.