The practice of inviting average people who have done extraordinary things to the State of the Union address began in 1982, with Ronald Reagan. These guests have sometimes been called "Lenny Skutniks" after the first person so recognized.

On January 13, 1982, Air Florida Flight 90 crashed into the Potomac moments after taking off from National Airport. As bystanders watched from the riverbanks and the bridge the plane crashed into, a few survivors were splashing in the icy water, and government employee Lenny Skutnik dove in and pulled one of the survivors to safety. He was not the only civilian to jump into the water - Roger Olian also risked hypothermia, but he was unable to physically carry anyone to shore. Nonetheless, both men received recognition as heroes, though only Skutnik attended the SOTU.

Two weeks after the crash and rescue, Reagan introduced Skutnik as part of a segment of the speech focused on regular American heroes. He said "We don't have to turn to our history books for heroes, they're all around us." He told the story of Senator Jeremiah Denton (also present), a POW during the Vietnam War who blinked the word "TORTURE" in Morse Code during a propaganda video, and then he told the story of Lenny Skutnik, noting especially that he was a government employee. Like in most SOTU speeches, Reagan wanted to uplift Americans with human interest stories, and hence his stories of these heroes.

Reagan invited another guest in 1984, a medic from the US invasion of Grenada, but that was the last "Lenny Skutnik" invited for 15 years. From 1999 to the present, though, in most years there has been an invited guest in the same style, usually honoring ordinary citizens who have done extraordinary things.

Sources:
1982 State of the Union transcript
Many resources are available on Palm 90, most recently this 40th anniversary article
Wikipedia: List of Lenny Skutniks

Personal note: This is obviously not my flair area (so not my professional study), but as my mother and I only narrowly avoided being on Palm 90, I have made amateur study of the event.