Realize, actualize, embody, incarnate, materialize, externalize, objectify, hypostatize, reify are the chief words in English meaning to give concrete or objective existence to something that has existed as an abstraction or a conception or a possibility.
They are seldom freely interchangeable, because their implications vary widely and their applications are largely determined by idiom.
Realize commonly implies emergence into the sphere of actual things (as of something that has been a dream, an ideal, a hope, or a plan).
The implication of attainment, of achievement, or of fulfillment is at times so strong in realize as to obscure or subordinate this fundamental idea of coming into existence.
Actualize, though sometimes used interchangeably with realize, is found chiefly in philosophical or technical writings with the implication of emergence (as of something that has existed only in potentiality) either into fullness or perfection of existence or into act or action.
Embody and incarnate sometimes imply investment with an outward or visible form of something abstract (as a principle, an idea, a trait, or a quality).
Materialize stresses emergence into the sphere of what is perceptible or tangible and usually presupposes prior vagueness, haziness, or elusiveness.
Externalize and objectify emphasize the projection of what is subjective (as a thought, an emotion, or a desire) so that it takes form apart from the mind.
Externalize often suggests a conscious or unconscious urge for expression or relief.
Objectify is more likely to suggest a conscious attempt to overcome the limitations of subjectivity and sometimes to contemplate one’s own mental processes.
Hypostatize and reify occur chiefly in philosophical and technical writing. They imply conversion by the mind of something that is a concept or abstraction into a thing that has real and objective even if not tangible existence.