Learn Spanish (Latin America): ¡Mi pasaporte había vencido!

Había vencido is the past perfect tense, which is used to talk about a past action that happened before another past action. In this sentence, using the past perfect emphasizes that the passport had already expired by the time the speaker realized it or tried to use it (for example, arriving at the airport).

I learned that vencer means 'to defeat' or 'to beat'. Why does it mean 'expired' here?

You are right that vencer means 'to defeat' in contexts like sports or battles. However, when talking about official documents (like a passport, license, or visa), contracts, or even food and medicine, vencer means 'to expire'.

If the noun was feminine, like licencia (license), would the verb change to había vencida?

No, it would still be había vencido. When you use the auxiliary verb haber (to have) to form perfect tenses, the past participle always ends in -o. It never changes to match the gender or number of the noun.