Hebrews 12:24 And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that spoke better things than that of Abel. 

‘Jesus the mediator’ – Christ became the mediator of the new covenant, that through His death sins could be remitted and men be given eternal inheritance. He became the Mediator between God and man (1Tim. 2:5), and through His mediation and intercession all blessings of grace shall come to us (Rom. 8:34; Heb. 7:25).

He is the mediator of a better covenant based upon better promises (8:6; 9:15; Matt. 26:28). By the atonement and the new covenant we have a personal approach to God which no man had by the law program (7:19; 10:19-23).  

Hebrews 7:22 states Christ was made a surety [Greek: enguos] meaning that He gave surety or bail. Christ became the guarantee that the benefits of the new covenant would be given to all men who meet the terms. In this sense, He is the mediator (8:6; 9:15).

‘Mediator’ [Greek: mesites] is a middle person to reconciles two parties at enmity – God and man.

‘Blood of sprinkling, that spoke better things than that of Abel.’ Only here and in 1Peter 1:2. It refers to the blood of Christ that speaks better things than the blood of Abel’s offering (11:4).