The note Julia passes to Winston, in George Orwell's novel 1984, reads "I love you." Given that neither one know each other at all, this could seem unbelievable. Essentially, one does not openly state their love to another without knowing the person.
That said, love is a mysterious thing. For some, the cliche "love at first sight" truly exists. Therefore, while they have not been formally introduced to each other, they have seen the other on multiple occasions.
Winston is very confused by the note. He believes that Julia, or "the girl" at this point, could be a spy, he is also drawn to helping others. Seeing her, at one point in the text, Winston feels extremely torn about helping her. In the end, Winston does agree to meet Julia. It seems that the three little words from a stranger forces Winston to throw caution to the wind. He, now, is both curious about the girl and the proclaimed love she has for him.