Fenrir, a brownish-gray timber wolf that appears several times in Advent Children, is seen as a symbol of Cloud's loneliness and his guilt for the deaths of two of his greatest friends: Aerith Gainsborough and Zack Fair, as well as for his other failures. This is not stated in the movie, but is mentioned in the Reunion Files, a "making of" book for Advent Children.
Source: Fenrir (Final Fantasy VII) - The Final Fantasy Wiki has more Final Fantasy information than Cid could research
There's a few more reasons/speculations about what the wolf was supposed to symbolize in the link, but I thought that paragraph that I copy/pasted was the most pertinent.
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