Your question seems to refer to the notes that Coleridge wrote to go alongside the text of the poem, where he describes the Albatross as a "good omen." Clearly, if you consider the state of the ship and the crew before and after the albatross appears, it can be seen why this was so true. The ship had been blown completely off course at the mercy of a tremendous ice storm. Then, it was surrounded by massive icebergs and thick fog that meant it had no escape or way to get out of the ice that blocked its every move. However, we are told that straight after the albatross appears, the ice breaks open and they are able to make their way out:
It ate the food it ne'er had eat,
And round and round it flew.
The ice did split with a thunder fit;
The helmsman steered us through!
The luck that the albatross brings is not limited to this escape however, for after this a "good south wind" comes up from behind the ship, giving it the motion that it needs to make its way away from all of the icebergs. The albatross proves to be a good omen indeed.
When it comes to stories about the ocean, sailors, or the sea in general there will always be a number of legends and rites associated to good or bad omens.
Birds are always good omens because they are the first sign that a sailor gets to realize that they are close to the shore, or that there is life close by, or even solid ground somewhere.
In the poem The Rime of the Ancient Mariner the sight of the Albatross through the blinding fog was a sign of good luck. The Albatross itself is a specific good sign for any person who is either lost at sea or fearing to not reach a destination because it is itself a sea bird: A seagull. Therefore, having its presence reinstates the sense of security among the sailors.
"The Rime of the Ancient Mariner" was written by Samuel Coleridge, who was one of the first-generation Romantic writers.
There are several characteristics of this literary movement, but the one that may overshadow all the others is a return to nature: all things of nature were to be appreciated and revered. In fact, it is this lesson that the mariner must learn, and in the learning, he is a changed and sad man because so much is lost before he learns the importance of nature by the story's end.
Coming through the fog, this bird travels and "plays" with the sailors, as they move northward through the snow and ice, and its company is considered a good omen. The sailors take it as a good sign, which may be primarily reflective of Coleridge's desire to praise this creature of nature.
Ultimately, the sailors convey their pleasure in the bird's company, believing that it is the presence of the bird that has made the breezes blow, something sailors desperately need. When the mariner speaks of what he has done, we learn why his shipmates felt the bird was a good omen:
For all averred, I had killed the bird
That made the breeze to blow. (93-94)