Aside from the definitions Webster1913 gives, a fimbria is also a short hair-like structure on a bacterium, used, en masse, for attaching to a surface or in forming pellicles. They are not used for locomotion.
It is also a small projection at the ends of the fallopian tubes, used to collect ova released from the ovaries into the tubes. (There are many, many fimbriae on the tubes).
Pronounced fim-bree-a or fim-bree-uh. From Latin, meaning threads or fringe.