What does the note that Julia gives to Winston say?
The note says "I LOVE YOU."
It's an odd sequence in the book, because other than Winston, the reader sort of assumes that all of the other characters are emotionless automatons. Perhaps anger and fear are felt, but love? That's not something the reader really sees. Nevertheless, Julia discreetly passes the note on to Winston while he is on his way to the bathroom. Julia is walking toward him, fakes a trip and a fall right in front of Winston, and Winston helps her get back up. It's a completely innocuous encounter, and Julia uses the moment to pass the note on to Winston.
Nevertheless it had been very difficult not to betray a momentary surprise, for in the two or three seconds while he was helping her up the girl had slipped something into his hand. There was no question that she had done it intentionally.
The next few pages are a lesson in building suspense, because the reader, and Winston, are not allowed to read the note immediately. Winston has to keep the note hidden, but deeply wants to read it. He has to unfold it within his pocket while using the bathroom. Then Winston has to casually toss the note on his pile at work, so as to make it look like a useless piece of scrap. Then he goes about working and tells himself to wait "five minutes" before looking at it. Only then does he read it, and he tries to make sure it looks like a normal part of his work routine.
The note said "I love you."
This happens in Part 2, Chapter 1.
Winston has left his cubicle to go use the bathroom when he sees Julia (he doesn't know her name yet at this point) coming down the hall toward him. Her arm is in a sling. As she comes toward him, she trips and falls and seems to have hurt herself.
Winston helps her up. When he does, she slips him a note. He takes it very carefully back to his cubicle and eventually reads it.
They have to be so secretive because the Party would not approve of them starting any kind of an affair like the one they are about to start.