The answer to your question can be found in chapter four of Tuck Everlasting. The stranger in question is the man in the yellow suit, and we are told the he came "strolling up" to the Foster's gate. Winnie happened to be playing in the front yard, and the stranger immediately engages her in conversation about catching fireflies.
Winnie is naive about a lot of things, but she is immediately wary about the strange man. His next question to Winnie asks her if she lives in that particular house. Winnie says "yes," and the man responds with another question. He wants to know how long Winnie and her family have lived in the house.
"Is this your house?" asked the man, folding his arms now and leaning against the gate.
"Yes," said Winnie. "Do you want to see my father?"
"Perhaps. In a bit," said the man. "But I'd like to talk to you first. Have you and your family lived here long?"
Winnie responds by telling the man that she has lived there "forever." The phrasing is typical little kid hyperbole, but the man in the yellow suit is immediately intrigued. He posits that Winnie must know everyone and everything about the area, and Winnie is forced to backpedal a bit. Winnie asks why the man is so curious about everyone and everything, and he admits that he is looking for a family.
The man lifted his eyebrows. "Oh," he said, "I'm looking for someone. A family."
The conversation is cut short as Winnie's grandmother comes out of the house, but readers will eventually figure out that the man in the yellow suit is looking for the Tuck family. He desires to figure out their secret to immortality because he wants to monetize it and make a fortune selling it to everybody.