(This article is technical and contains some nuance, which might be hard for people not acquainted with this topic to grasp. Therefore, if you have not yet believed in Jesus Christ as Savior, I recommend reading the article What Must I Do to Be Saved? first, and then coming back to this article later. Feel free to reach out to me if you have any questions about this article or any suggestions.)
The Gospel is the proclamation concerning the Lord Jesus, who according to Scripture is the Christ, the Son of God, which means that He is God incarnated as a man, the Savior of the world and the only name given unto men whereby we must be saved, who is also the resurrection and the life, the One who has the words of eternal life, and the One whom God has set upon His throne to be the Judge of the living and the dead. In addition, the Gospel is the historical event that announces Jesus Christ's vicarious life and death whereby He performed His all-sufficient work of salvation for His people, His victory over death through His resurrection, and His authority as Lord over all heaven and earth. From the sinner's point of view, the Gospel manifests God's justice, unveils the only way to propitiate His wrath, reveals His righteousness, shows His love in dealing so graciously with mankind, and exposes the sinner's need of a mercy that cannot be earned or appropriated. The Gospel is also the good news whereby the sinner may be saved, which by believing he sets to his seal that God is true and righteous, and by recognizing the divine righteousness and peculiar glory revealed therein, he comes to be assured that God only is his Savior in Jesus Christ, all to the praise of the glory of His grace. The Gospel is the message that God commands all men to believe, which if believed, guarantees to the sinner that God chose him beforehand in Christ to be a vessel of mercy in order to show throughout eternity the surpassing riches of His grace in kindness toward him in Christ Jesus.
Although the nature of "faith" (Gr. pistis, which can also be translated as "belief," being the cognate noun of the verb "to believe") should be obvious from the description of the Gospel given above, because theologians of all religions and denominations have utterly distorted the meaning of "faith" and have turned it into various things that only bear the name "faith," ranging from a "life of faithful living" to an "appropriating instrument," the word "faith" can mean a 1,001 different things depending on whom you ask. However, what these 1,001 different things have in common is that they turn faith into works or require faith to perform works. However, what "faith" (hereinafter used interchangeably with the noun "belief" and the verb "believe") means in every other realm of life is exactly what it means in the Bible, namely, a persuasion of the mind that its propositional object (i.e., the content of a declarative statement or something, such as a person, who represents the content of the declarative statements advanced by him or her) is true, and this will be demonstrated below from the Scripture. However, first it necessary to demonstrate that the object of belief is indeed a proposition and can never grammatically be a command to do something. To demonstrate this, it is sufficient to show the awkwardness that results when we try to make a command the object of belief. For example, it doesn't make sense to say, "I believe 'Repent!'" A command such as "Repent and believe the Gospel" points us to the Gospel, but the command itself is neither the Gospel, nor can it be used as the object of belief. In contrast, as mentioned above, the object of belief must always be a proposition. The content of the Gospel is a proposition, so it can be the object of belief, as in the sentence "I believe the Gospel." Believing a proposition means to be convinced that the content of the proposition is true. In the case of the Gospel, it means being convinced that the content of the Gospel is true, even as Abraham and Sarah were convinced that the propositions advanced by God were true (Rom. 4:21-22, Heb. 11:11). If you believe the content of the Gospel described above (i.e., you are persuaded that it is true), then you are saved. In contrast, if you despise the content of the Gospel and think it is too small of a thing to believe that Jesus is the Christ, the Son of God, and instead attempt to appropriate the benefits of the Gospel to yourself through some mysterious "heart work" ascribed to the Holy Spirit, or try to acquire salvation by dedicating your life to God, undergoing some ritual such as water baptism, or endeavor to mix anything you believe God is doing in your life with Christ's all-sufficient work at the cross, then you shall be condemned as a person who has sought to establish his own righteousness in place of the divine righteousness accomplished once and for all by God in Christ.
The Apostles confirm the description of faith given above. For example, John described what it means to "believe" as follows, "If we receive the witness of men, the witness of God is greater; for the witness of God is this, that He has borne witness concerning His Son. The one who believes in the Son of God has the witness in himself; the one who does not believe God has made Him a liar, because he has not believed in the witness that God has borne concerning His Son" (1 John 5:9-10, and see also 1 Thess. 2:13, as well as 2 Thess. 1:7-10 and 2:10-14 where obeying the Gospel is basically equated with believing the apostles testimony). Receiving the witness of God (i.e., the propositions that constitute the witness) is exactly the same as receiving the witness of men, except for the fact that the witness of God is more authoritative. But notice how the Apostle equates "receiving witness concerning His Son" with "believing in the Son," where "receiving" corresponds to "believing" and "witness concerning His Son" corresponds to "the Son" (i.e., the propositions represented by Him or advanced by Him). This is evident from John's description that "believing" results in "having the witness in himself," meaning that he received the witness (i.e., the propositions that constitute the witness) as being true (i.e., he was persuaded of the truth of the propositions). People who don't receive the witness as being true have made God a liar, meaning that they disbelieved the propositions that constituted the witness advanced by Him. Likewise, John the Baptist tells us, "What He has seen and heard, of that He bears witness; and no man receives His witness. He who has received His witness has set his seal to this, that God is true" (John 3:32-33), and then immediately after this says, "He who believes in the Son has eternal life" (John 3:36a). Similarly, Jesus described what it means to "believe" in John 3:11-12, "Truly, truly, I say to you, we speak that which we know, and bear witness of that which we have seen; and you do not receive our witness. If I told you earthly things and you do not believe, how shall you believe if I tell you heavenly things?" What we see here is that the Apostle John, John the Baptist, and Jesus all describe the verb "believe" as a persuasion of the mind that a proposition is true. In the Gospel of John, to believe in Jesus means to be convinced that the propositions represented by Him or advanced by Him are true, namely that He is the Christ, the Son of God who is the Savior of the world (John 20:29-31, John 4:42, 1 John 4:14). In confirmation of this, the only passage in the Bible that defines "faith" says, "Now faith is the assurance of things hoped for, the conviction of things not seen" (Heb. 11:1). In other words, faith is being assured and convinced that things (described in propositions presented to the mind), although currently unverifiable by the human senses, are true. Applying this understanding of belief to the Gospel of John, none of us saw the crucifixion and resurrection of Jesus Christ, but when we believe that the eyewitness accounts (i.e., the propositions) given by the Apostles in the New Testament are true, we literally fulfill Jesus' words "Blessed are they who did not see, and yet believed" and are assured and convinced that "things hoped for but not seen" are true, by which we come to know that we have "life in His name" (John 20:28-31, 1 John 5:13).
Belief in the objective truth of the Gospel brings with it joy and assurance. Many people can explain important truths of the Gospel, but because they don't have a correct understanding of belief, they never actually believe the Gospel. Many people think that they can receive the benefits of the Gospel by mixing belief with other things, such as trusting in Jesus, establishing a relationship with Him, or appropriating His salvific work to themselves. In other words, they think that those things are elements of belief. But they are not. Rather, they nullify belief and introduce self righteousness and mysticism. The fact is that no one can appropriate the benefits of the Gospel. Sinners can't bribe God through their efforts to trust in Jesus, rest in Jesus, or surrender to Jesus, nor can they compel Him, as if He were their slave, to save them for Jesus' sake because they supposedly performed some appropriating act in their hearts. Rather, God is sovereign and He confers His salvation and benefits on sinners according to His own mercy and grace, and by causing them to believe the Gospel, He is causing them to understand what He accomplished for them as their only Savior. Believe the Gospel and let the truth of the Gospel be your joy and sufficiency that overflows in much praise and thankfulness to God.