From BiblePortal Wikipedia

Webster's Dictionary [1]

(1): ( n.) The act of demonstrating; an exhibition; proof; especially, proof beyond the possibility of doubt; indubitable evidence, to the senses or reason.

(2): ( n.) An expression, as of the feelings, by outward signs; a manifestation; a show.

(3): ( n.) The exhibition and explanation of a dissection or other anatomical preparation.

(4): ( n.) (Mil.) a decisive exhibition of force, or a movement indicating an attack.

(5): ( n.) The act of proving by the syllogistic process, or the proof itself.

(6): ( n.) A course of reasoning showing that a certain result is a necessary consequence of assumed premises; - these premises being definitions, axioms, and previously established propositions.

Vine's Expository Dictionary of NT Words [2]

1: Ἀπόδειξις (Strong'S #585 — Noun Feminine — apodeixis — ap-od'-ike-sis )

lit., "a pointing out" (apo, "forth," deiknumi, "to show"), a "showing" or demonstrating by argument, is found in  1—Corinthians 2:4 , where the Apostle speaks of a proof, a "showing" forth or display, by the operation of the Spirit of God in him, as affecting the hearts and lives of his hearers, in contrast to the attempted methods of proof by rhetorical arts and philosophic arguments.

King James Dictionary [3]

Demonstration n.

1. The act of demonstrating, or of exhibiting certain proof. 2. The highest degree of evidence certain proof exhibited, or such proof as establishes a fact or proposition beyond a possibility of doubt, or as shows the contrary position to be absurd or impossible. 3. Indubitable evidence of the senses, or of reason evidence which satisfies the mind of the certainty of a fact or proposition. Thus we hold that the works of nature exhibit demonstration of the existence of a God. 4. In logic, a series of syllogisms, all whose premises are either definitions, self-evident truths, or propositions already established. 5. Show exhibition. 6. In anatomy, the exhibition of parts dissected.