Stephanie V. answered 06/13/19
Dedicated to Teaching the Humanities!
In this case, the ancient mariner is simply incredibly old, as he is described as being grey and withered at the beginning of the poem. However, the events of the poem can be interpreted to mean that he is now immortal. Essentially, even while he suffered through his penance for shooting the albatross, what he saw was so wondrous, frightening, and bizarre (the dead crew, the voices he heard, the Hermit, etc.) that he feels compelled to tell the tale forever, however long he will live. Given the supernatural tone of the poem, which was not uncommon for Romantic-era poetry, he very well could be compelled by God to tell his frightening tale until the end of eternity.