I do not know all the details, but Elder Haight had experienced a stroke or heart attack or something and had to be taken to the hospital. Some surgery was performed and during this time he had visions.
Consider this paragraph from his talk:
I heard no voices but was conscious of being in a holy presence and atmosphere. During the hours and days that followed, there was impressed again and again upon my mind the eternal mission and exalted position of the Son of Man. I witness to you that He is Jesus the Christ, the Son of God, Savior to all, Redeemer of all mankind, Bestower of infinite love, mercy, and forgiveness, the Light and Life of the world. I knew this truth before—I had never doubted nor wondered. But now I knew, because of the impressions of the Spirit upon my heart and soul, these divine truths in a most unusual way.
To have your spirtual cup refilled, go read Elder Haight's talk as well as Elder McConkie's. As you read them, consider what an Apostle is ... a special witness of Jesus Christ.