At an archaeological dig, the matrix is the soil surrounding the site. Biologists use the phrase "nuclear matrix" to refer to the material left behind after DNA is extracted from a cell's nucleus. A matrix is an environment or structure in which something originates or develops.
Matrix, related to the Latin word for "mother," originally meant "pregnant animal" or "breeding female" and was later generalized to mean "womb." Today, matrix includes any nurturing or supportive setting or substance usually within the fields of math and the sciences — except in the cinematic trilogy starring Keanu Reeves, of course. Matrixes is an acceptable plural form, but you can use matrices if you want to show off your knowledge of Latin noun endings.