The model in question is a 1967 Lancia Fulvia Sport 1.3 Zagato that's owned by auto appraiser and journalist Donald Osborne. It's a good thing that he's around too because Jay is pretty clearly out of his element when discussing this beautiful coupe. The two of them end up having a fairly long conversation about not just this car but also the whole history of Lancia.
According to Osborne, the Zagato-bodied version was the top model of the Fulvia range, and the famous coachbuilder made about 7,000 of them between 1965 and 1972. The styling featured a gorgeous mix of razor sharp creases and shapely curves to really set the design apart from its contemporaries, and power came from a 1.3-liter V4 spinning the front wheels.
It's fascinating to watch Leno learning about the car for the first time over the course of the video and then start picking out little details about the Fulvia that he likes. Get educated right along with him in this interesting episode looking at one of the great Lancias.