Nephi desired to see the things which his father saw, and to know the interpretation thereof. Here is a list of symbols and their meaning as given to Nephi in his vision, also the event he saw that related to each symbol.
The love of God, which sheddeth itself abroad in the hearts of the children of men. It is the most desirable above all things. (11:21-22) The interpretation was declared by Nephi after seeing the infant Savior with his mother, Mary.
Rod of Iron:
The word of God, which leads to the tree of life. The interpretation was given after Nephi saw the Son of God going forth among the children of men, and many fall down at His feet and worship Him. (11:24-25)
Fountain of Living Waters:
The Love of God, or the tree of life. The fountain of living waters is only mentioned once and has the same meaning as the tree. The rod of iron leads to both (11:25)
Large and Spacious Building:
The world and the wisdom thereof; the pride of the world; vain imaginations and the pride of the children of men. The interpretation was given in connection with the house of Israel - multitudes of the earth - fighting against the twelve apostles of the Lamb. The interpretation was also given in connection with the destruction of the Nephites. It falls, and the fall thereof is exceedingly great. (11:34-36; 12:15-19)
Fountain of Filthy Water, River and Its Depths:
The depths of hell. The interpretation was given while Nephi saw his seed destroyed by the seed of his brethren. (12:15-19)
Mists of Darkness:
The temptations of the devil, which blind the eyes and harden the hearts of the children of men, and leads them away into broad roads, that they perish and are lost. The interpretation was given while Nephi saw his seed destroyed by the seed of his brethren. (12:15-19)
Great and Terrible Gulf:
The word of the justice of the Eternal God. It divides the large and spacious building from the tree of life. The interpretation was given while Nephi saw his seed destroyed by the seed of his brethren. (12:15-19)