Definition of Propitiation:

Propitiation is a two-part act:

 
1. appeasing the wrath of God
 
2. being reconciled to God  
   

Definition of Propitiation from Vine's Expository Dictionary of New Testament Words:  

A-1,Verb,2433,hilaskomai  
was used amongst the Greeks with the significance "to make the gods propitious, to appease, propitiate," inasmuch as their good will was not conceived as their natural attitude, but something to be earned first. This use of the word is foreign to the Greek Bible, with respect to God, whether in the Sept. or in the NT. It is never used of any act whereby man brings God into a favorable attude or gracious disposition. It is God who is "propitiated" by the vindication of His holy and righteous character, whereby, through the provision He has made in the vicarious and expiatory sacrifice of Christ, He has so dealt with sin that He can show mercy to the believing sinner in the removal of his guilt and the remission of his sins.  
 
Thus in Luke 18:13 it signifies "to be propitious" or "merciful to" (with the person as the object of the verb), and in Heb. 2:17 "to expiate, to make propitiation for" (the object of the verb being sins); here the RV, "to make propitiation" is an important correction of the AV, "to make reconciliation." Through the "propitiation" sacrifice of Christ, he who believes upon Him is by God's own act delivered from justly deserved wrath, and comes under the covenant of grace. Never is God said to be reconciled, a fact itself indicative that the enmity exists on man's part alone, and that it is man who needs to be reconciled to God, and not God to man. God is always the same and, since He is Himself immutable, His relative attitude does change towards those who change. He can act differently towards those who come to Him by faith, and solely on the ground of the "propitiatory" sacrifice of Christ, not because He has changed, but because He ever acts according to His unchanging righteousness.  
 
The expiatory work of the Cross is therefore the means whereby the barrier which sin interposes between God and man is broken down. By the giving up of His sinless life sacrifically, Christ annuls the power of sin to separate between God and the believer.  
 
In the OT the Hebrew verb kaphar is connected with kopher, "a covering" (see MERCY SEAT), and is used in connection with the burnt offering, e.g., Lev. 1:4; 14:20; 16:24, the guilt offering e.g., Lev. 5:16,18, the sin offering, e.g., Lev. 4:20,26,31,35, the sin offering and burnt offering together, e.g., Lev. 5:10; 9:7, the meal offering and peace offering, e.g., Ezek. 45:15,17, as well as in other respects. It is used of the ram offered at the consecration of the high priest, Ex. 29:33, and of the blood which God gave upon the altar to make "propitiation" for the souls of the people, and that because "the life of the flesh is in the blood," Lev. 17:11, and "it is the blood that maketh atonement by reason of the life" (RV). Man has forfeited his life on account of sin and God has provided the one and only way whereby eternal life could be bestowed, namely, by the voluntary laying down of His life by His Son, under Divine retribution. Of this the former sacrifices appointed by God were foreshadowings.  
 
b-1,noun,2435,hilasterion  
akin to A, is regarded as the neuter of an adjective signifying "propitiatory." In the Sept. it is used adjectivelly in connection with epithema, "a cover," in Exod. 25:17; 37:6, of the lid of the ark (see MERCY SEAT), but it is used as a noun (without epithema), of locality, in Exod. 25:18-22; 31:7; 35:12; 37:7,8,9; Lev. 16:2,13-15; Num. 7:89, and this is its use in Heb. 9:5.  
 
Elsewhere in the NT it occurs in Rom. 3:25, where it is used of Christ Himself; the RV text and punctuation in this verse are important: "whom God set forth to be a propitiation, through faith, by His blood." The phrase "by His blood" is to be taken in immediate connection with "propitiation." Christ, through His expiatory death, is the Personal means by whom God shows the mercy of His justifying grace to the sinner who believes. His "blood" stands for the voluntary giving up of His life, by the shedding of His blood in expiatory sacrifice, under Divine judgment righteously due to us as sinners, faith being the sole condition on man's part.  
 
Note: "By metonymy, 'blood' is sometimes put for 'death,' inasmuch as, blood being essential to life, Lev. 17:11, when the blood is shed life is given up, that is, death takes place. The fundamental principle on which God deals with sinners is expressed in the words 'apart from shedding of blood,' i.e., unless a death takes place, 'there is no remission' of sins, Heb. 9:22.  
 
"But whereas the essential of the type lay in the fact that blood was shed, the essential of the antitype lies in this, that the blood shed was that of Christ. Hence, in connection with Jewish sacrifices, 'the blood' is mentioned without reference to the victim from which it flowed, but in connection with the great antitypical sacrifice of the NT the words 'the blood' never stand alone; the One Who shed the blood is invariably specified, for it is the Person that gives value to the work; the saving efficacy of the Death depends entirely upon the fact that He Who died was the Son of God." * [* From Notes on Thessalonians by Hogg and Vine, p. 168.]  
 
b-2,noun,2434,hilasmos  
akin to hileos ("merciful, propitious"), signifies "an expiation, a means whereby sin is covered and remitted." It is used in the NT of Christ Himself as "the propitiation," in 1 John 2:2; 4:10, signifying that He Himself, through the expiatory sacrifice of His Death, is the Personal means by whom God shows mercy to the sinner who believes on Christ as the One thus provided. In the former passage He is described as "the propitiation for our sins; and not for ours only, but also for the whole world." The italicized addition in the AV, "the sins of," gives a wrong interpretation. What is indicated is that provision is made for the whole world, so that no one is, by Divine predetermination, excluded from the scope of God's mercy; the efficacy of the "propitiation," however, is made actual for those who believe. In 1 John 4:10, the fact that God "sent His Son to be the propitiation for our sins," is shown to be the great expression of God's love toward man, and the reason why Christians should love one another. In the Sept., Lev. 25:9; Num. 5:8; 1 Chron. 28:20; Ps. 130:4; Ezek. 44:27; Amos 8:14.

Definition of Propitiation from Strong's Exhaustive Concordance:  

2435 ιλαστηριον hilasterion hil-as-tay'-ree-on  
AV-propitiation 1, mercyseat 1; 2  
1) relating to an appeasing or expiating, having placating or expiating force, expiatory; a means of appeasing or expiating, a propitiation  
1a) used of the cover of the ark of the covenant in the Holy of Holies, which was sprinkled with the blood of the expiatory victim on the annual day of atonement (this rite signifying that the life of the people, the loss of which they had merited by their sins, was offered to God in the blood as the life of the victim, and that God by this ceremony was appeased and their sins expiated); hence the lid of expiation, the propitiatory  
1b) an expiatory sacrifice  
1c) an expiatory victim 

2434 ιλασμος hilasmos hil-as-mos'  
AV-propitiation 2; 2  
1) an appeasing, propitiating  
2) the means of appeasing, a propitiation  

Ro 3:25  Whom God hath set forth to be a propitiation <2435> through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;  
1Jo 2:2  And he is the propitiation <2434> for our sins: and not for ours only, but also for the sins of the whole world.  
1Jo 4:10  Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation <2434> for our sins.