Learn Italian: Sembrava che l'autunno fosse stato molto mite. - It seemed that the autumn had been very mild.

Sembrava (It seemed) is a past-tense expression of opinion or appearance, which requires a subjunctive in the dependent clause. We use the Pluperfect Subjunctive (fosse stato or "had been") because the autumn being mild happened before the moment it "seemed" that way. If the two things happened at the same time ("It seemed that autumn was mild"), you would use the Imperfect Subjunctive (fosse).

Why does this sentence use fosse as the auxiliary verb instead of avesse?

To form the Pluperfect Subjunctive, you use the imperfect subjunctive of either avere or essere, plus a past participle. The main verb in the second clause of this sentence is essere (to be). In Italian, essere always uses itself as its auxiliary in compound tenses! Therefore, "had been" becomes fosse (imperfect subjunctive of essere) plus stato (past participle of essere).

If the season were feminine, like l'estate (the summer), would stato change?

Yes! Whenever a compound tense uses essere as its auxiliary verb, the past participle must agree in gender and number with the subject. Since l'autunno is masculine singular, we use stato. If it were l'estate (feminine singular), the sentence would be "Sembrava che l'estate fosse stata molto mite."