John 15:4 has the phrase "Live in me, and I will live in you." What does it mean to live in someone or to live in God?
Apostle Paul in the book of Ephesians continues this thought known as the “Christocentric” principle. This principle introduces Christ in us the hope of Glory. To me it means that we live our lives with Christ being the center of it, and by doing so we find ourselves taking on a new life in Christ. As Paul stated in Acts 17:28, “In Him we live, and move, and have our being.” This life is made possible by the “indwelling” holy spirit that Jesus said he would send to us so that we could live in Him, and He in us.
The meaning is given in the context of John 15:1-7. There, Jesus is likening himself to a vine. His illustration is simple: as long as the branches remain in the trunk of the vine, then they continue to take nourishment from the trunk.
So if we continue to depend on Christ and not be moved away from him, then he will feed our spiritual lives and we will flourish in the knowledge of him.
Living in God is, practically speaking, to live as though there is a God who is a personal God who loves and cares for us, and we are to return that affection appropriately with obedience to him and his word.
This abiding, or continuing, can be likened to patiently building up a relationship, like a marriage where the spouses have gone through tough times and are continuing in marriage instead of jumping ship quickly.
While the two answers you already have answer the meaning of those statements, I thought it might also be useful to tell how they are accomplished, perhaps if not for your sake for the sake of someone else who is caused to wonder by your question.
The cohabitation of Spirits is routinely known as having a relationship with God. As with any relationship it is born of familiarity. In other words the better you know someone the better your relationship becomes, and it is certainly no different with God.
Since God is not like a neighbor who we can go to their home and visit with them, we must visit with God in different ways. There are two ways in which we get to know God better and thereby have him live in us and us in him.
God left us the Bible which is an extensive look at the persons of God and God's personality(for lack of a better term on my part).
Secondly God communicates to us through prayer.
The more we know about the Bible the better we can know God, therefore a conscientious reading or study program is an absolute necessity. By following God's actions and reactions in the Bible we learn what he desires of us, as well as what we can expect from him.
So how does God communicate to us in prayer? He does that through answering prayer, an if you have ever experienced God answering a prayer in a way which can only be explained as an act of God you know what I am talking about, and if you haven't you might need to closely examine your prayers, because Jesus promised.
John 14:13 And whatever you ask in My name, that I will do, that the Father may be glorified in the Son.
John 14:14 If you ask anything in My name, I will do it.
John 15:16 You did not choose Me, but I chose you and appointed you that you should go and bear fruit, and that your fruit should remain, that whatever you ask the Father in My name He may give you.
John 16:23 "And in that day you will ask Me nothing. Most assuredly, I say to you, whatever you ask the Father in My name He will give you.
John 16:24 Until now you have asked nothing in My name. Ask, and you will receive, that your joy may be full.
John 16:26 In that day you will ask in My name, and I do not say to you that I shall pray the Father for you;
verse 15:16 may hold the key in that God will not give you frivolous things, but will give you everything needed to live a Christian life. And it may come to you in the form of hard work.
Hope this helps.