In English, my never changes: my book, my keys. In Spanish, mi (my) and tu (your) change with the thing you own — they add an -s when there's more than one:

Owner	one thing	more than one
yo — my	mi libro, mi casa	mis libros, mis llaves
tú — your	tu libro, tu casa	tus libros, tus llaves

The owner plays no part: Marcos and Marina both say mis llaves (my keys), because there's more than one key.

The possessive replaces the article: mi casa, never la mi casa. And watch the accent: tu (your) has none, tú (you) has one — Tú tienes tu libro. You have your book.