Paul states clearly how one can receive salvation:

But what does it say? "The word is near you, in your mouth and in your heart"—that is, the word of faith which we are preaching, that if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved; for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation. (Rom 10:8-10)

Paul indicates that a person's salvation is based on what a person believes in their heart and what they confess with their mouth. Jesus speaks of the heart and its relationship to the mouth in His response to the Jews:

Either make the tree good and its fruit good, or make the tree bad and its fruit bad; for the tree is known by its fruit. You brood of vipers, how can you, being evil, speak what is good? For the mouth speaks out of that which fills the heart. The good man brings out of his good treasure what is good; and the evil man brings out of his evil treasure what is evil. But I tell you that every careless word that people speak, they shall give an accounting for it in the day of judgment. For by your words you will be justified, and by your words you will be condemned. (Matt 12:33-37)

Taken together with Jesus' call, "repent for the kingdom of God is at hand" (Mark 1:14; Matt 4:17), Jesus is referring to repentance at the heart level.

Genuine repentance is directed towards God. It involves a significant judgment of oneself and prompts one to turn to God; genuine repentance includes the concept of a radical change – a conversion.

The biblical concept of "repentance" is with this meaning of "to change one's mind." This places an emphasis on the thought and will of a person, and it is in this context that the concept of conversion arises. From a "change of mind" to a "change of behavior," a person "turns" his will from himself to God, or a person "turns away" from sin to "turns" towards holiness.

The biblical concept of "confess" essentially means "to say the same" and signifies an agreement to the historical truth about Jesus (the Son of God who died in atonement for mankind's sin and proved His deity with His resurrection) and the truth about the sinful state of human beings.

Confronted with these facts, confession is the verbal acknowledgment of repentance that has taken place within one's heart and a declaration of commitment to Jesus Christ, Savior and Lord.

For deeper study:

What is genuine repentance?

What does the term "confess" mean in the New Testament?

Finding Forgiveness For Your Sin (R. Alcorn)

An invitation to salvation