Who are the "elect" the Bible talks about?
"Peter, an apostle of Jesus Christ, to those who reside as aliens, scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia, who are chosen according to the foreknowledge of God the Father, by the sanctifying work of the Spirit, to obey Jesus Christ and be sprinkled with His blood: May grace and peace be yours in the fullest measure" (I Peter 1:1-2).
The elect is the group of people God chose to sanctify for the purpose of obeying Christ.
The sprinkling of the blood is a reference to the dedication to a covenant and cleansing. "For if the blood of bulls and goats and the ashes of a heifer, sprinkling the unclean, sanctifies for the purifying of the flesh, how much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, cleanse your conscience from dead works to serve the living God? And for this reason He is the Mediator of the new covenant, by means of death, for the redemption of the transgressions under the first covenant, that those who are called may receive the promise of the eternal inheritance" (Hebrews 9:13-15).
Those who obey Christ are his followers. "Do you not know that to whom you present yourselves slaves to obey, you are that one's slaves whom you obey, whether of sin leading to death, or of obedience leading to righteousness? But God be thanked that though you were slaves of sin, yet you obeyed from the heart that form of doctrine to which you were delivered. And having been set free from sin, you became slaves of righteousness" (Romans 6:16-18).
Those sanctified are the people set apart for a special purpose for God. "And such were some of you. But you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus and by the Spirit of our God" (I Corinthians 6:11).
Therefore, the elect is just another name for Christians. It refers to the fact that Christians are God's chosen people. "But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light" (I Peter 2:9). Under the Old Covenant, Israel was God's chosen people, but under the New Covenant, it is a type of people, not their heritage, whom God has chosen to be His special people.
"What then shall we say to these things? If God is for us, who can be against us? He who did not spare His own Son, but delivered Him up for us all, how shall He not with Him also freely give us all things? Who shall bring a charge against God's elect? It is God who justifies. Who is he who condemns? It is Christ who died, and furthermore is also risen, who is even at the right hand of God, who also makes intercession for us" (Romans 8:31-34).
"Therefore, as the elect of God, holy and beloved, put on tender mercies, kindness, humility, meekness, longsuffering; bearing with one another, and forgiving one another, if anyone has a complaint against another; even as Christ forgave you, so you also must do" (Colossians 3:12-13).
"Therefore I endure all things for the sake of the elect, that they also may obtain the salvation which is in Christ Jesus with eternal glory" (II Timothy 2:10).