This is the 12589th most frequent Portuguese word.
teu
"Teu" means "your" (singular, informal) in English.
In this sentence, 'teu' functions as an adjective modifying 'sorriso' to express possession.
Teu sorriso ilumina meu dia.
Your smile brightens my day.
Here, 'teu' is used as a possessive pronoun to indicate that the book belongs to the second person singular to whom the speaker is addressing.
Este é o teu livro favorito.
This is your favorite book.
Here again, 'teu' is a possessive pronoun used to indicate that the support is provided by the addressed individual.