From St. Thomas Aquinas, Summa Theologiae, 3, q. 26 a. 1:
Properly speaking, the office of a mediator is to join together and unite those between whom he mediates: for extremes are united in the mean [medio]. Now to unite men to God perfectively belongs to Christ, through Whom men are reconciled to God, according to 2 Corinthians 5:19: “God was in Christ reconciling the world to Himself.” And, consequently, Christ alone is the perfect Mediator of God and men, inasmuch as, by His death, He reconciled the human race to God. Hence the Apostle, after saying, “Mediator of God and man, the man Christ Jesus,” !1 Timothy 2:5) added: “Who gave Himself a redemption for all.”
He goes on in the following article to say this:
We may consider two things in a mediator: first, that he is a mean; secondly, that he unites others. Now it is of the nature of a mean to be distant from each extreme: while it unites by communicating to one that which belongs to the other. Now neither of these can be applied to Christ as God, but only as man. For, as God, He does not differ from the Father and the Holy Ghost in nature and power of dominion: nor have the Father and the Holy Ghost anything that the Son has not, so that He be able to communicate to others something belonging to the Father or the Holy Ghost, as though it were belonging to others than Himself. But both can be applied to Him as man. Because, as man, He is distant both from God, by nature, and from man by dignity of both grace and glory. Again, it belongs to Him, as man, to unite men to God, by communicating to men both precepts and gifts, and by offering satisfaction and prayers to God for men. And therefore He is most truly called Mediator, as man.
That’s something unique about Christianity: God and us at a meeting place, and a meeting person.