the reinforcement phase
The reinforcement is the dispersed, usually stronger and stiffer partner embedded in the matrix: the straw in the mud brick, the steel rebar in concrete, the glass or carbon fibers in a resin. It is the part that actually carries most of the load or blocks the cracks.
Reinforcement can be particles, short fibers, long continuous fibers, or sheets, and it is chosen for high stiffness and strength, and often low density. Load transfers from matrix to reinforcement across the interface, and the reinforcement takes the majority because it is much stiffer (at equal strain, stress is proportional to modulus). For example, carbon fiber at 230 GPa in epoxy at 3 GPa carries, at the same strain, about 77 times the stress of the matrix per unit area.
The reinforcement's shape and orientation, not just its material, decide the properties: continuous aligned fibers give huge stiffness along their length but little across it; random short fibers or particles give more isotropic but smaller gains. More reinforcement (higher volume fraction) usually means stiffer and stronger, but harder to process and often less tough.
Steel rebar in a concrete beam: the concrete matrix is strong in compression but weak in tension, so the steel bars sit where the beam is stretched and carry the tension the concrete cannot.
Reinforcement need not be fiber; particles count too. It is the dispersed, load-carrying phase.
Reinforcement does not automatically mean fiber, and more is not always better: beyond an optimum, poor wetting and voids can make the composite weaker rather than stronger.