The speaker refers to Autumn as the "Season of mists and mellow fruitfulness" because he wishes to honor and compliment the season whose hallmarks some might see as less beautiful than "the songs of spring." On the contrary, this speaker feels that Autumn has its own "music" that is absolutely as lovely as Spring.
One aspect of fall that makes it so attractive is how ripe all of the harvests are. The vines are "load[ed] and bless[ed] / With fruit," and fat, juicy apples bend "the moss'ed cottage-trees." The season and the sun "swell the gourd, and plump the hazel shells / With a sweet kernel," and the multitude of "flowers for the bees" make them think that warm days will last forever. There is such a sense of abundance and plenty, and beauty in ripeness. Further, the "drows[y] . . . fume of poppies" and the "last oozings [of] hours" help to explain why all this "fruitfulness" feels so "mellow."
In the final stanza, the speaker references the "barred clouds [which] bloom [on] the soft-dying day, / And touch the stubble-plains with rosy hue." If you can imagine an early fall sunset with misty clouds overhead that help to paint the sky with rose and salmon tones, then Keats's reference to "mists" becomes a bit clearer too.