Imagine how James Potter felt when he found out that his parents had been killed. His parents, who had taught him right and wrong, and who had never cared that he was friends with Sirius Black, or that he was chasing a muggle born around, trying to date her.
Imagine the agony, the torture he went through. He was only seventeen, and now he had no parents. He was expected to just mope for a while and then get over it. But he couldn't, because they were his parents. More than that, they were like parents to Sirius as well. Imagine Sirius when James' parents died. He had never gotten along with his family, and had run away when he was sixteen. They had taken him in, and put a roof over his head, and treated him like he was their own. They weren't offended when he found a new place, but still invited him over to dinner every Sunday.
Imagine Remus, who had always looked up to them as great examples, and who was thankful that they saw him as a person, and not as a monster. They knew he was a werewolf, and they didn't care.
And imagine poor Harry, never knowing his grandparents, or being able to experience their love and kindness.