There are several different genres that use orchestration. If it's jazz, we generally call it "big band," although there is also something called "orchestral jazz", as well as wide repertoire of jazz-influenced classical music. Similarly, there is an actual subgenre called "orchestral rock" (think Led Zeppelin's "Kashmir").
But this particular song is "chamber pop", a style combining pop sensibilities with lush orchestral accompaniments. It was pioneered by the Beatles (Sgt Pepper, "Yesterday") and the Beach Boys (Pet Sounds). Controversial producer Phil Spector is also associated with the genesis of the style, for instance in his epic collaboration with Tina Turner, "River Deep, Mountain High."
For more recent variations, you might compare singer Chris Mills, pop composer Ben Folds, who often books tours where he appears with local orchestras, and cult classic band XTC's Apple Venus 1.