Back in the 1970's the first two Voyager spacecraft were known to become the first two objects to leave the solar system. Carl Sagan and others convinced NASA to include a gold record/disk with sounds and sights of the world. The disk had descriptions of Earth, and a map as to where the space craft had come. At the speed of these Voyager spacecraft, it would take 50,000 years to get to the nearest star.
Well, after just a few years in space, one of the craft comes near an inhabited planet. The natives read the disk and send an ambassador to visit Earth. He had a invite (the record) but did not RSVP. As he enters the Earth's atmosphere, NORAD doesn't know who he is, so they shoot his space craft down.
It crashlands near a lake front home in Wisconsin. Even though the craft is damaged, the traveler survives and goes to the nearest house.
The resident, Jenny Hayden (Karen Allen), lives alone, as she lost her husband in an accident 1-1/2 years ago. While she sleeps, the alien, in the form of a small blue light comes into the house, find a lock of the husband's hair, and through genetic manipulation, grows into a full sized man in only 5 minutes. Growing bones, tendons and muscles, makes some noise, and wakens Jenny. She sees a small child grow into a man right there on her living room floor. Imagine her surprise when the new full sized man looks just like her dead husband, The Starman (Jeff Bridges).
After her initial scare she comes to trust him (it). She knows this being is not her husband, but sure looks it, and begins to act like him. However, this being will only survive about 3 days in this form. So the home world will come for him in 3 days.
He convinces Jenny, to drive him to Winslow, Arizona. At first, she thinks she is being kidnapped. But, as he learns our language and a few of our customs, she becomes sympathetic to his cause, and helps him in his journey.
The government, however has different plans. They now have his damaged spacecraft, and quickly figure out what form the Starman has taken, and trace his car across the country. The government team, lead by Mark Shermin (Charles Martin Smith) is very crafty at tracing his moves. By the time they catch up to him in Arizona, the chase becomes a fight to the death, as the government wants to dissect the poor man!
Jenny saves the day with an insider in the government, and Starman makes his appointment with his own kind. A little like ET returning home, only with adult emotions.