a polymer-matrix composite
The most common fiber composites: a plastic matrix holding glass or carbon fibers. Fiberglass boats and bathtubs (glass fibers in polyester, GFRP) and black carbon-fiber bike frames and jet parts (carbon fibers in epoxy, CFRP) are all polymer-matrix composites.
The matrix is usually a thermoset (epoxy, polyester, vinyl ester) that cures into a rigid network, or sometimes a thermoplastic. Epoxy (about 3 GPa, cures around 120 to 180 degrees C) wets fibers well and bonds strongly. GFRP is cheap, tough, corrosion-proof, and a good electrical insulator; CFRP is stiffer and lighter (higher specific stiffness) but pricier. Aramid (Kevlar) fibers add impact and abrasion resistance.
PMCs dominate because they are light, corrosion-resistant, easy to mould into complex shapes, and give superb strength-to-weight. Their limits are honest: the polymer matrix softens and creeps with heat (typically usable only to about 150 to 250 degrees C), can absorb moisture, and is hard to recycle, especially thermosets, which cannot simply be remelted.
A modern airliner wing skin is CFRP: carbon fibers in epoxy give the stiffness and strength of metal at much lower weight, cutting fuel burn, but it is cured in an autoclave and cannot be re-melted for recycling.
Light and strong, but the polymer matrix caps the service temperature and blocks easy recycling.
The carbon-fiber part is a composite: carbon fibers plus a polymer matrix. The shiny black weave you see is held together entirely by resin, and it is the resin (and heat) that limit its service temperature.