This is the 1476th most frequent Arabic word.
التى
"التى" means "who" or "which" (feminine singular relative pronoun).
The word "التي" is used here as a relative pronoun to connect the noun "المرأة" (the woman) to the clause "رأيتها اليوم" (whom I saw today).
المرأة التي رأيتها اليوم كانت لطيفة.
The woman whom I saw today was kind.
"التي" acts as a relative pronoun connecting the noun "الفرصة" (the opportunity) to the relative clause "كنت أبحث عنها" (that I was looking for).
هذه هي الفرصة التي كنت أبحث عنها.
This is the opportunity that I was looking for.
Here, "التي" introduces the relative clause "زرتها" (that I visited) and relates it to the noun "المدينة القديمة" (the old city).