The first two listed below are found in the New Testament. Understanding their meanings helps us better comprehend God's expectations of us.
Agapao (verb) is a special word representing the divine love of God toward His Son, human beings in general and believers. It is also used to depict the outwardly focused love God expects believers to have for one another. Agapao (including its noun form, agape) is "the characteristic word of Christianity, and since the Spirit of revelation has used it to express ideas previously unknown, inquiry into its use, whether in Greek literature or in the Septuagint, throws but little light upon its distinctive meaning in the N[ew] T[estament] . . ."
This special type of Christian love, "whether exercised toward the brethren, or toward men generally, is not an impulse from the feelings, it does not always run with the natural inclinations, nor does it spend itself only upon those for whom some affinity is discovered" (Vine's Complete Expository Dictionary of Old and New Testament Words, "Love").
Reflecting the fact that human marriage is modeled after the divine relationship between Christ and the Church, husbands are told to love their wives with this kind of outgoing, selfless love (Ephesians 5:25-32 Ephesians 5:25-32  Husbands, love your wives, even as Christ also loved the church, and gave himself for it;
 That he might sanctify and cleanse it with the washing of water by the word,
 That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish.
 So ought men to love their wives as their own bodies. He that loves his wife loves himself.
 For no man ever yet hated his own flesh; but nourishes and cherishes it, even as the Lord the church:
 For we are members of his body, of his flesh, and of his bones.
 For this cause shall a man leave his father and mother, and shall be joined to his wife, and they two shall be one flesh.
 This is a great mystery: but I speak concerning Christ and the church.
American King James Version×).
This kind of love is perhaps best expressed in Jesus Christ's statement in John 15:13 John 15:13Greater love has no man than this, that a man lay down his life for his friends.
American King James Version×, "Greater love [agape] has no one than this, than to lay down one's life for his friends." Jesus Himself perfectly exemplified this kind of love throughout His lifetime, continually giving of Himself and His time and energies to serve others and ultimately offering up His life as a sacrifice for all of humanity. This is the kind of love God wants each of us to exemplify in our lives and particularly in our marriages.
Phileo (verb) means "'to have ardent affection and feeling'—a type of impulsive love" (Nelson's New Illustrated Bible Dictionary, 1995, "Love"). This is the natural, human type of love and affection that we have for a friend and is often defined as "brotherly love."
In John 21:15-16 John 21:15-16  So when they had dined, Jesus said to Simon Peter, Simon, son of Jonas, love you me more than these? He said to him, Yes, Lord; you know that I love you. He said to him, Feed my lambs.
 He said to him again the second time, Simon, son of Jonas, love you me? He said to him, Yes, Lord; you know that I love you. He said to him, Feed my sheep.
American King James Version×, Jesus asked Peter if he loved Him with the agapao type of love and Peter responded that he had the normal human phileo type of love for Him. Later, after receiving the Holy Spirit, Peter would be able to genuinely demonstrate agapao-type godly love, serving others throughout his lifetime and making the ultimate sacrifice in martyrdom.
Eros (noun) refers to sexual, erotic love or desire.
True love, as explained in the Bible, isn't focused on oneself and one's feelings or emotions, but is instead outwardly focused on others—wanting to best serve and care for them. True love is beautifully described in 1 Corinthians 13:4-8 1 Corinthians 13:4-8  Charity suffers long, and is kind; charity envies not; charity braggs not itself, is not puffed up,
 Does not behave itself unseemly, seeks not her own, is not easily provoked, thinks no evil;
 Rejoices not in iniquity, but rejoices in the truth;
 Bears all things, believes all things, hopes all things, endures all things.
 Charity never fails: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away.
American King James Version×: "Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres. Love never fails" (NIV).