How do these lines of dialogue move the plot along?

You need to quote the lines for me.

"I'm sorry--" began the visitor.

"Is he hurt?" demanded the mother wildly.

The visitor bowed in assent. "Badly hurt," he said quietly, "but he is not in any pain."

"Oh!" said the old woman, clasping her hands. "Thank goodness for that! Thank--"

She broke off suddenly as the sinister meaning of the assurance dawned upon her

and she saw the awful confirmation of tears in the other's averted face.

That's all the lines for you.