Jackson's Limousine was a car that Jackson Curtis owned, spending his former life as a chauffeur.
In the film, Jackson uses this Limo instead of his station wagon which the engine starter was broken. So, Jackson drives his children Noah and Lily to Yellowstone (though in real life he would have to board a plane to get to it in a short time) and back. He later uses it to drive Alec and Oleg to the airport to board a small private plane. Just after doing it, he picks up Charlie Frost's radio signals, informing of a massive earthquake that's about to hit the city. Jackson goes to his household and grabs Noah, Lily, his former wife Kate and her boyfriend Gordon, and narrowly drives over extremely dangerous 'obstacle courses' before making it to the airport.
The car was left in bad condition and was abandoned after the Curtis family boarded a Cessna plane and presumably fell into the large ditch created by the San Andreas Fault.