The fiber optic is used to connect long distance switches, central offices and SLCs (subscriber loop carriers, small switches in pedestals in subdivisions or office parks or in the basement of a larger building).
LANs (local area networks) use fiber optics primarily in the backbone but increasingly to the desk. The LAN backbone often needs longer distance than copper cable (Cat 5/5e/6) can provide and of course, the fiber offers higher bandwidth for future expansion. Most large corporate LANs use fiber backbones with copper wire to the desktop. Fiber to the desk can be cost effective if properly designed.
Lots of other networks use fiber. CCTV is often on fiber for it's distance capability. Industrial plants use lots of fiber or distance and noise immunity. Utilities use it for network management, liking its immunity to noise also. The military uses it because it's hard to tap or jam. Airplanes use it for that reason too, but also like the lighter weight of fiber
ABOUT SPEED---
It was over a year after Gigabit Ethernet (GbE) became available on fiber optics that it finally become available on Cat 5e. It took another couple of years before GbE on copper became significantly less expensive. In order to get GbE to work over Cat 5e, the electronics must be very complicated, and consequently as expensive as fiber. A newer version is in the wings, awaiting a Cat 6 standard, but that means the version running over Cat 5e will be obsolete before it even gets started! Finally, we went to a major distributor's seminar on advanced cabling recently and the copper marketing guy told us to go fiber for GbE.