The function of a capacitor with the fluorescent lamp
Figure 1. A typical fluorescent lamp circuit with capacitor on mains input. Source: Illumination - types of lamps.

Fluorescent lamps form an inductive load on the AC mains supply. As a result large installations of such lamps suffer a poor power factor and resultant voltage drop. Adding a capacitor to each lamp corrects the power factor bringing it back close to unity (1.0). This solves the problem of associated voltage drop and also, for large energy users, eliminates power factor surcharge on the bills - for that part of the load at least.

It is possible to omit the capacitor on the individual lamps and to centralise them in the switch room and automatically switch in as many as required to keep the power factor within acceptable limits.