Sandy knows what it is to be invisible, even in plain sight.
After millennia of being unheard, he knows it. Even now they can see him, he can only produce pictures to convey his points. He is easily forgotten, even by those he holds closest, when there is something distracting them, he fights just to be noticed. Even though the children can see him, his presence is strongest the moment before they rest, and he is dismissed as a part of his own creation.
So when Bunny attacks that particular point, Jack is not the only one in the room who freezes, who thinks of centuries without notice. The Sandman recovers first, alerting North to take care of the situation, but now he knows, he cannot help but feel that all Jack's sarcastic quips and mischievous behaviour are purely, somewhere deep down, a cry for help that hits Sandy keenly. He's made that call, for sure, and no one has ever answered. He wants to comfort the winter spirit, let him know he's not alone, and it is why he jumps to explain. But Jack cannot hear his 'voice', cannot understand his form of speech, and turns away, isolating himself unknowingly from Sandy's sympathy.
He is sad, but no matter – he will help them fight, he will try to get through to Jack that now, although he has been failed before, he is not alone, they will stand together and fight together, and they will win.
The last thing he hears, sees, is Jack's frantic call, the first of the Guardians to try to rescue him, though Sandy knows it is too late.
It goes dark. He feels his power moving against his will, bending good dreams to nightmares, unfulfilling, unwholesome, empty. He is powerless to stop it.
And then he feels a belief, flickering, and jumps towards it, desperate to escape what seems to be his fate. He doesn't know how, but he feels it, how the child manages to use his power to turn the tide against Pitch, to allow him to be reborn, and feels somehow that Jack was the one who ultimately saved him, brought him back.
To repay him, the Sandman sends dreams in the form of snowball fights, twirling snowflakes and the beauty of a landscape covered in snow. When he is finished, he descends back to the ground, and he and Jack share a smile: this time, Sandy thinks that the winter spirit might understand, even if there are miles to go in the trust and friendship they may eventually form.
Jack, I understand what it is to be invisible. You are no longer alone.
Sandy feels like he finally realises that fact, even though no words, silent or spoken, had passed between them.
Of all the four initial Guardians, Sandy intrigues me the most, and also happens to be the one who is explained the least. It just seems to me, that without a voice he would also be quite used to being ignored, so probably feels the most affinity with Jack. As in, Bunny and North have their holidays when kids remember about them, if no other time, and Tooth is remembered every time a child loses a tooth, but Sandy's effect is much more subtle - often, people can't even remember what they dreamt about, and it could be that people dream and forget they ever dreamt, so I can see even though he is believed in, he is almost invisible.