The importance of Gershwin lies in the fact that he created a very personal style,unmatched by any other composer. It is hard to describe what exemplifies his style,as it includes Jazz,Broadway,Classical.
The crux is how to actually play his music.
Very often it is played in a sentimental way,sometimes its misunderstood as being very jazzy,but it is more complicated than that.
Gershwin himself wrote often very precise indications down how he wanted his pieces to be performed ,and they make a lot of sense.
But the trouble is that he deviates a lot from some of his own notations.
And turns around tempi and phrasings to create something quite new.
He also was not satisfied with his style ,he tried to learn and improve and even wanted to study with Maurice Ravel,who famously turned him down by saying :"why do you want to become a 2nd rate Ravel,stay being a first rate Gershwin."
His music has an irresistible charm, is staggeringly original despite using harmonics and patterns that were used by many.
I particularly adore the Concerto in F and his Songbook and the piano solo version of his Rhapsody in Blue.
Here is the essence of his style.
Watts plays Gershwin - Songbook (13 Songs) Audio + Sheet music - YouTube