In "The Rime of the Ancient Mariner," the albatross is a good omen for sailors and sometimes even represented the soul of a lost sailor. So, to kill the albatross is to bring bad luck. Hung on the mariner's neck, the albatross becomes a symbol of his thoughtless crime. The mariner doesn't seem to have any malice when he killed the albatross. However, he must deal with the consequences of his action. His penance is to continue to travel, presumably forever, to different lands to retell his tale. He is doomed to an eternity of warning others to avoid his mistakes.
And till my ghastly tale is told,
This heart within me burns.
I pass, like night, from land to land;
I have strange power of speech;
That moment that his face I see,
I know the man that must hear me:
To him my tale I teach. (584-590)
This is why Life-in-Death won the dice game. Had Death won, the mariner would have died. Instead, the mariner is subject to a kind of life in death, traveling forever in order to tell his tale.
Keep in mind the epigraph, from Thomas Burnet, which begins, "I readily believe that there are more invisible than visible Natures in the universe." He goes on to say, "Meanwhile I do not deny that it is helpful sometimes to contemplate in the mind, as on a tablet, the image of a greater and better world, lest the intellect, habituated to the petty things of daily life, narrow itself and sink wholly into trivial thoughts." That invisible, better world is the idealistic or spiritual world beyond human perception. Thus, the symbols in the mariner's story could reflect spiritual as well as physical meanings.
The voyage is symbolic of the mariner's life: his path to sin and his subsequent repentance.
As the ship turns around Cape Horn, the southernmost tip of South America, the mariner and his crew head north towards the Sun rising in the east (on their right). The Sun is a symbol of God and this image is veiled by the foreboding fog which is indicative of an evil presence eclipsing the goodness of the Sun. (The Sun also becomes a symbol of, perhaps God's, punishment as it contributes to the drought.
The glorious Sun uprist:
Then all averred, I had killed the bird
That brought the fog and mist. (98-100)
The ship becomes like a prison. Stuck in the middle of the ocean with no drinking water, it is another punishment.
Water, water, every where,
And all the boards did shrink;
Water, water, every where,
Nor any drop to drink. (119-122)
The ghost ship, which Death and Life-in-Death arrive in, is simply symbolic of retribution, death, evil, and punishment.
The crew of the mariner's ship might be compared to the wedding party. The former is associated with the killing of an innocent life (albatross) and the latter is associated with a celebration of life.
"Rime" is a frost coating of ice. In poetry, ice can be symbolic of death. In this poem, the rime (ice) is similar to the foreboding fog and the lifelessness of the South Pole. It is symbolizes the mariner's sin or crime and his upcoming punishment; note the similarity of the words: (c)rime. So, the rime is the crime and the invisible (spiritual or demonic) elements manifested via fog and ice. The rime is also the mariner's story (his penance of having to retell his story), the "rhyme"/poem itself.