Possessive adjectives show possession. In Spanish, we have different ones for one thing possessed or more than one thing possessed.
First-Person Singular: Mi (My)
Second-Person Singular: Tu (Your, singular)
Third-Person Singular: Su (His / Her)
First-Person Plural: Nuestro / Nuestra (Our)
Second Person Plural: Vuestro / Vuestra (Your, plural)
Third Person Plural: Su (Their)
First-Person Singular: Mis (My)
Second-Person Singular: Tus (Your, singular)
Third-Person Singular: Sus (His / Her)
First-Person Plural: Nuestros / Nuestras (Our)
Second Person Plural: Vuestros / Vuestras (Your, plural)
Third Person Plural: Sus (Their)
Some examples: mi casa, mis carros, sus tíos, nuestras casas, tus abuelos.
Notice how the subject of the sentence is the object or the animal possessed: Mi gato es rojo uses the third person conjugation (él), not the first person conjugation (yo). The subject is the cat, not me.
When we are not using possessives and saying who the person is, in Spanish we cannot use [‘s] (Juan’s house). We have to say la casa de Juan (the house of Juan).