In English, my never changes. In French it changes with the thing you own — its gender, and whether there's one or more:

• mon frère — my brother (masculine)
• ma sœur — my sister (feminine)
• mes parents, mes clés — my parents, my keys (any plural)

The owner plays no part. Marcos and Marina both say ma maison, because maison is feminine — and both say mon téléphone, because téléphone is masculine. In the plural there's no gender at all: mes for everything.