What do Evangelical Protestants mean by "receive Jesus"? In conservative Evangelical Churches, one often hears exhortations to become "saved" by "accepting" or "receiving" Jesus "into your heart", often accompanied by an invitation to pray a special prayer of salvation. 

According to Evangelical Biblical interpretation, what exactly, in Biblical terms, does it mean to "receive" Jesus into your heart?
For Evangelicals, "receiving Jesus" can be considered to be functionally equivalent to one or more of the following:


Regeneration
Being born again 
Receiving the (indwelling) Holy Spirit
Being justified by faith
Being adopted into the family of God
Being saved
Conversion
Making a decision
Praying through


Evangelicalism is somewhat of a moveable feast and different Evangelicals will have their own favoured terminology - sometimes treating the other terms listed here as synonyms, and sometimes emphasizing distinctions between them.

This doctrine stands at the core of Evangelicalism, and as such there are many more scriptural passages that have been cited in support of it than is appropriate to reproduce here. Nevertheless, here are ten passages that are very commonly linked with it:

Ezekiel 36:26-27


  I will give you a new heart and put a new spirit in you; I will remove from you your heart of stone and give you a heart of flesh. And I will put my Spirit in you and move you to follow my decrees and be careful to keep my laws. 


John 3:3


  Jesus replied, “Very truly I tell you, no one can see the kingdom of God unless they are born again.


John 14:16-17


  And I will ask the Father, and he will give you another advocate to help you and be with you forever— the Spirit of truth. The world cannot accept him, because it neither sees him nor knows him. But you know him, for he lives with you and will be in you.


Romans 5:1-2


  Therefore, since we have been justified through faith, we have peace with God through our Lord Jesus Christ, through whom we have gained access by faith into this grace in which we now stand. And we boast in the hope of the glory of God.


Romans 8:8-10


  Those who are in the realm of the flesh cannot please God. You, however, are not in the realm of the flesh but are in the realm of the Spirit, if indeed the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, they do not belong to Christ. But if Christ is in you, then even though your body is subject to death because of sin, the Spirit gives life because of righteousness.


Romans 8:14-16


  For those who are led by the Spirit of God are the children of God. The Spirit you received does not make you slaves, so that you live in fear again; rather, the Spirit you received brought about your adoption to sonship. And by him we cry, “Abba, Father.” The Spirit himself testifies with our spirit that we are God’s children.


Romans 10:9-10


  If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved.


2 Corinthians 5:17


  Therefore, if anyone is in Christ, the new creation has come: The old has gone, the new is here!


Colossians 1:26-27


  the mystery that has been kept hidden for ages and generations, but is now disclosed to the Lord’s people. To them God has chosen to make known among the Gentiles the glorious riches of this mystery, which is Christ in you, the hope of glory.


Revelation 3:20


  Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with that person, and they with me.