Six times in New Testament (Galatians 3:19-20; Hebrews 8:6; Hebrews 9:15; Hebrews 12:24; also the verb, Hebrews 6:17, Greek "mediated," emesiteusen, "by an oath," "interposed as mediator between Himself and us with an oath"; Jesus is the embodiment of God's mediating oath: Psalm 110:4). One coming between two parties to remove their differences. The "daysman" (Job 9:33) who "lays his hand upon both" the litigants, in token of his power to adjudicate between them; mokiach, from yakach, "to manifest or reprove"; there is no umpire to whose authoritative decision both God and I are equally amenable. We Christians know of such a Mediator on a level with both, the God-man Christ Jesus (1 Timothy 2:5). In Galatians 3:20 the argument is, the law had angels and Moses (Deuteronomy 5:5) as its mediators; now "a mediator" in its essential idea (ho mesitees, the article is generic) must be of two parties, and cannot be "of one" only; "but God is one," not two.
As His own representative He gives the blessing directly, without mediator such as the law had, first by promise to Abraham, then to Christ by actual fulfillment. The conclusion understood is, therefore a mediator cannot pertain to God; the law, with its mediator, therefore cannot be God's normal way of dealing. He acts singly and directly; He would bring man into immediate communion, and not have man separated from Him by a mediator as Israel was by Moses and the legal priesthood (Exodus 19:12-24; Hebrews 12:19-24).
It is no objection to this explanation that the gospel too has a Mediator, for Jesus is not a mediator separating the two parties as Moses did, but at once God having "in Him dwelling all the fullness of the Godhead," and man representing the universal manhood (1 Corinthians 8:6; 1 Corinthians 15:22; 1 Corinthians 15:28; 1 Corinthians 15:45; 1 Corinthians 15:47; 1 Corinthians 15:24; 2 Corinthians 5:19; Colossians 2:14); even this mediatorial office shall cease, when its purpose of reconciling all things to God shall have been accomplished, and God's ONENESS as "all in all" shall be manifested (Zechariah 14:9). In 1 Timothy 2:4-5, Paul proves that "God will have all men to be saved and (for that purpose) to come to the knowledge of the truth," because "there is one God" common to all (Isaiah 45:22; Acts 17:26).
Romans 3:29, "there is one Mediator also between God and man (all mankind whom He mediates for potentially), the man (rather 'man' generically) Christ Jesus," at once appointed by God and sympathizing with the sinner, while untainted by and hating sin. Such a combination could only come from infinite wisdom and love (Hebrews 1; 2; Hebrews 4:15; Ephesians 1:8); a Mediator whose mediation could only be effected by His propitiatory sacrifice, as 1 Timothy 2:5-6 adds, "who gave Himself a vicarious ransom (antilutron) for all." Not only the Father gave Him (John 3:16), but He voluntarily gave Himself for us (Philemon 2:5-8; John 10:15; John 10:17-18). This is what imparts in the Father's eyes such a value to it (Psalm 40:6-8; Hebrews 10:5). (See PROPITIATION; RANSOM; ATONEMENT; RECONCILIATION.)
Fausset, Andrew Robert M.A., D.D., "Definition for 'mediator' Fausset's Bible Dictionary".