The Mariner kills the albatross because he associated the lack of wind with it. At first all the men thought the bird was good luck since a good wind blew and they moved swiftly. Then, the wind died and they blamed the bird. THe sailors cheered when the Mariner killed the bird which is symbolic of animal abuse. By killing the bird, he is disrespecting all of nature--a sin since the poem states: all creatures great and small the lord God created them all.
Once the Mariner "blesses the snake unaware," then he begins the long trek back to being forgiven and living out the rest of his life wandering the earth and teaching others how to treat mother nature and all her creatures.