of a material by the formation of a precipitate
The way this works is two materials should form a solution at high temperatures and a heterogeneous mixture at lower temperatures. The lattice spacings of the materials should be different as well.
The materials (usually metals) are heated to form a solution, then cooled so the solute precipitates as small crystals. The material is then aged at high temperature--aging allows the size of the precipitated particles to grow.
If the particles are too small, the strength of the material is not increased by as much, since dislocations may easily move around the particles. If the material is overaged, grain boundaries may form around the precipitate due to lattice mismatch.
This technique is also known as age hardening.