The kataan people made a portable "holodeck". Picard lived in this "faster-than-realtime"-holodeck, and everything around him was constructed to let the observer learn about the culture of the Kataan.
From the episode:
Years later, an extremely old Kamin is playing with his grandchild,
Meribor's son. He laments that his grandson deserves a long and full
life, but like the rest of their world he will not survive. Kamin goes
along with everyone else to view "the launching", which only he seems
not to know about. Kamin asks, "What is it they're launching?"
His daughter, Meribor: "You know it, father. You've already seen it."
"Seen it? What are you talking about? I haven't seen any missile."
Batai: "Yes, you have, old friend. Don't you remember?"
Kamin turns to see his old friend, Batai, but in the prime of his
life. Batai explains, "You saw it just before you came here. We hoped
our probe would encounter someone in the future – someone who could be
a teacher, someone who could tell the others about us."
"Oh... oh, it's me... isn't it? I'm the someone. I'm the one it finds.
That's what this launching is – a probe that finds me in the future!"
Stunned, Kamin turns and sees Eline, glowing in youthful beauty, with
the rest of his family. She says, "The rest of us have been gone a
thousand years. If you remember what we were...and how we lived...then
we'll have found life again."
The observation made by Picard (or any person who would pick up the probe-signal) would have lived this holodeck-version of a life with the Kataan's like for example Data lives the life of Sherlock Holmes in the same manner.