The first time Harry hears Professor Snape call him son, he stops and freezes. He's not used to hearing a loving moment from anyone before. It doesn't help him that this word "son," gives him some feelings that he never had before. It's validating to him but it's also how Professor Snape called him "son," that he never had before.
He told him to "stay close, son."
Harry froze, of course, because it's a foreign word. A foreign that implies love. The word hangs around for them and yet it felt right too. Harry responds back to this, by saying, "thanks."
But also, this moment helps him to throw out the anger, the hurt, the neglect he had from the Dursleys because he now knows that someone loves him. And he knows how to name this.