Technicolor is the idea that the Higgs boson of the Standard Model is not a fundamental particle but a composite state of two fermions. These fermions are held together by a new force called Technicolor. The name stems from the idea that this technicolor is similar to the color charge of quantum chromodynamics.
Technicolor is a proposed solution for the hierarchy problem of the standard model of particle physics.
A great explanation of the motivation behind technicolor models can be found in section V of The fifth force by James D. Bjorken. He draws nicely the analogy between present day Higgs physics and what would have happened if the correct theory of strong interactions were still unknown.