As you sing or listen to this Hymn, you will see the words superimposed over the picture of the composer, Horatio G. Spafford.
As is noted on the webpage accompanying the music -- there is a reason for the writing of this Hymn. It is:
"Horatio G. Spafford was known as a sincere, devout Christian. He was the father of four daughters, an active member of the Presbyterian church, and a loyal friend and supporter of D. L. Moody and other evangelical leaders of his day.
In November 1873, Spafford decided to take his entire family to Europe for a vacation, intending also to assist Moody in his evangelistic work once he arrived there. However, Spafford was unexpectedly detained in Chicago due to urgent business concerns, but decided to send his family aboard the S.S. Ville du Harve as scheduled. Midway through the trans-Atlantic voyage, S.S. Ville du Harve was struck by the English vessel Loch Earn and eventually foundered. Spafford's four daughters—Anna, eleven; Maggie, nine; Bessie, seven; and Tanetta, two—were among the 226 who perished in the aftermath. Mrs. Spafford, one of the few who were spared, sent her husband the heartbreaking telegram: "Saved alone."
Spafford immediately sailed for England to join his grief-stricken wife. As his ship passed the approximate location where his daughters had drowned, his deep sorrow mingled with his unwavering faith in God's goodness caused him to compose this hymn."
When you die, it can also be "well with your soul" IF you believe in The Lord God Jesus Christ and have accepted His gift of eternal life provided for you by His death which paid the penalty for all your sins.
For God so loved the world (and you and me) that He gave His only begotten Son (Jesus Christ) -- that whosoever believes in Him (Jesus) shall not perish (and go to Hell) but shall have eternal life (in Heaven).