"Fiberglass" is typically a shorthand for "Fiber Reinforced Plastic" FRP or "Glass Reinforced Plastic" GRP and is often used interchangibly with these terms. What fiberglass really is, is fibers of glass (Duh). These thin glass fibers are gathered together to make [fiberglass cloth]?. The glass used falls into two varieties (E-Glass and S-Glass but it is really glass that does not differ much from window glass. Strangely enough the thin fibers make a flexible material that is quite strong.
There is also a common tendancy to mistake fiberglass for the resin used to binding the fibers together. These resins are typically epoxy, vinylester or polyester. The resins are actually the plastic refered to in FRP and GRP. When combined with a liquid resin the glass, which starts off looking white, becomes clear. It is a common mistake to say "fiberglass" when what people really mean is the resin.