On an immediate level, the thrush symbolises freedom and emotion.
It was in the sun, they in the shade.
This symbolises how the thrush is free to live its life as it chooses - literally 'free as a bird' - while Winston and Julia are subjugated by the oppressive society they live in.
For whom, for what, was that bird singing? No mate, no rival was watching it. What made it sit at the edge of the lonely wood and pour its music into nothingness?
This suggests that the bird is singing not just because of some social obligation, but out of pure emotion. It also awakens feelings in Winston:
It was as though it were a kind of liquid stuff that poured all over him and got mixed up with the sunlight that filtered through the leaves. He stopped thinking and merely felt.
After this, Winston finally begins to feel sexual desire for Julia: his inhibition or lack of feeling which prevented them from making love earlier is gone.
The whole description of the thrush and its singing is in sharp contrast to the description of human society which makes up most of the book. It seems carefree, happy, artistic, beautiful, emotional - none of these are adjectives one might have used to describe anything else in the book so far. This contrast appears even more starkly when Winston's thoughts wander briefly away from the thrush and back to human surveillance:
He wondered whether after all there was a microphone hidden somewhere near. He and Julia had spoken only in low whispers, and it would not pick up what they had said, but it would pick up the thrush. Perhaps at the other end of the instrument some small, beetle-like man was listening intently — listening to that.
And much later on, shortly before their arrest, Winston and Julia's thoughts go back to the thrush again, and once again we see the contrast between it and the Party society.
‘Do you remember,’ he said, ‘the thrush that sang to us, that first day, at the edge of the wood?’
‘He wasn’t singing to us,’ said Julia. ‘He was singing to please himself. Not even that. He was just singing.’
The birds sang, the proles sang. The Party did not sing.
One strange aspect of this passage is that the description of the thrush's song is actually
incorrect. The song thrush (
Turdus philomelos), the main species of thrush found in Britain, has a song which is distinctive because of its constant
repetition: every set of notes it makes is repeated over and over again, at least 2 or 3 times and often more. Every British birdwatcher knows this.
https://www.youtube.com/watch?v=G53oH-MI9qU
So when I first read 1984, the following description of the thrush's song (emphasis mine) was horribly jarring to my suspension of disbelief:
The music went on and on, minute after minute, with astonishing variations, never once repeating itself, almost as though the bird were deliberately showing off its virtuosity.
What's the explanation for this apparent mistake? Well, Occam's razor would say it actually is a simple mistake, and that Orwell wasn't aware of the defining characteristic of the song of one of the commonest British songbirds, despite choosing that song to describe at length in his novel. But what if there's a darker and more subtle explanation?
Perhaps the thrush isn't a real thrush at all. Perhaps the Party has created believable fake birds to do some of their spying for them. Perhaps the unrealistic song of the thrush was an early indication that, even then, the Party was watching Winston and Julia's every move (as we discover much later on, they had certainly been watched since long before this scene).
Or perhaps I'm thinking of the wrong dystopian novel and have jabberjays on the brain.
I'm fairly sure I've read this theory elsewhere, and that perhaps it was even made explicit in one of the film adaptations of 1984. But I can't find any reference to it now, so my justification above, based only on the text and a knowledge of ornithology, will have to do.