Using Fiber over UTP is normally done for distance due to the extremely high costs. Fiber is used for various applications, backbone applications being one. In some cases fiber is used inside a building (for instance server to server connections, where the highest levels of security are needed, or for storage area networks). The electronics that operate over fiber are higher than those for copper as an optical conversion is needed to do this. In some cases, fiber may provide lower latency over copper counterparts, but that is dependent on the electronics and protocols in use. Also in some areas where noise is an issue, fiber is not affected by electromagnetic or RF noise.
Distance is the main factor, especially with emerging standards for newer UTP standards, because standard cat5 cable can only go 100 meters, (328 feet), before you start having signaling problems and it is also susceptible to Electromagnetic interference.
You can also use fiber instead of UTP if you are going from building to building and there are storm issues. at one company that I worked at they installed fiber between two buildings even though they were very close because lightning storms had damaged equipment hooked to the copper UTP lines before.