Gatsby's car, outsized and ostentatious, represents Gatsby's flamboyant gestures, love of the material world, and huge capacity to dream.

We learn that the car is very large and both green on the inside, like a "conservatory," and painted a creamy color that people describe as yellow. For instance, George Wilson calls it a "nice yellow" car, and a person who witnesses the accident at the end of the novel describes it as

" a yellow car," he said, "big yellow car. New."

Green and yellow are both colors associated with Gatsby. Green, such as the green light at the end of Daisy's pier, represents Gatsby's dreams and desires, while yellow or cream represents his money.

Buying a huge car—"rich cream color, bright with nickel"—is typical of and represents Gatsby's tendency to make large gestures. He doesn't just throw parties, he throws the biggest and best parties possible, just as he lives in a huge mansion and owns expensive shirts in every color in the rainbow. He never does things by halves.

The car being "bright with nickel" and "new" represents Gatsby's nouveau riche status. If Tom is associated with polo, horses, and old money, Gatsby is symbolized by the car, still new in the 1920s, and the brash new 1920s wealth it symbolizes.

Finally, it is significant that the mirrors on the car "mirrored a dozen suns." The sun is a symbol of hope in this novel, and the "dozen" suns that the car reflects represent the outsized capacity of Gatsby to hope and dream. Nick comes to admire Gatsby's boundless capacity to dream amid the "foul dust" that surrounds him.

Gatsby's car is a very flashy, ostentatious set of wheels. As such, it represents the nouveau riche, the new-money crowd of West Egg to which he belongs.

As Gatsby wants to impress people with his phenomenal wealth, he figures that if you've got it, you need to flaunt it. And so it's not enough for Jay to own a regular automobile; he has to have an oversized car of “monstrous length,” “swollen here and there,” with all kinds of boxes designed for storage space.

By owning such a monstrosity of a car, Gatsby is showing off his wealth. Just like the lavish parties he throws at his mansion on a regular basis, he wants to impress people. At the same time, one can easily imagine a member of the old-money East Egg elite looking down their noses at Gatsby's car, dismissing it as frightfully vulgar, a surefire sign of someone with lots of money but with no class or taste.

But this is probably the only way that Gatsby can make an impression. He doesn't have an impressive pedigree or a good family name. All he has is money and lots of it. That being the case, he's left with no choice but to flash the cash if he's going to get other people to notice him. And what better way to do that than to invest in a flashy car?

Gatsby's car is very much a symbol of the man himself.  Nick, indeed, first describes it as "gorgeous," just like Gatsby appears to others: well-dressed, well-spoken, well-educated.  He appears to be perfect, just like his car.

However, Nick goes on to describe it as

[...] swollen here and there in its monstrous length with triumphant hat-boxes and supper-boxes and tool-boxes, and terraced with a labyrinth of wind-shields that mirrored a dozen suns.  Sitting down behind many layers of glass in a sort of green leather conservatory, we started to town.

Words like "swollen" and "monstrous" have quite negative connotations, especially to describe such a "gorgeous" vehicle, alerting us to the fact that something more is going on here.  "Swollen" is often used in connection to some kind of infection or illness, and "monstrous" connotes something grotesque, deformed.  This might lead us to imagine someone who is puffed up, someone who has made something of themselves that is completely different from who they really are.  Gatsby himself has become larger and stranger by his acquisition of all the material goods that seem to swell his car and draw attention to his giant size.  

However, the labyrinthine, multi-layered glass seems like so many beautiful ways to distract from something or hide it altogether.  Instead of clearly revealing the person within, they mirror "a dozen suns," protecting the identity within the labyrinth.  Just as the car's windshields hide its driver, so does Gatsby's elaborate persona hide the person he really is.

The best way to answer the question is to give the description of it. Here is what the text says:

Gatsby's car was a ''rich cream color, bright with nickel, swollen here and there in its monstrous length with triumphant hatboxes and supper-boxes and tool-boxes, and terraced with a labyrinth of windshields that mirrored a dozen suns'

Again, the text says:

''labyrinth of windshields that mirrored a dozen suns.''

Based on these descriptions, it is clear that the Rolls Royce is over the top, excessive, and meant to impress. The second quote show the glitz and glamor. All of this fits Gastby's personality and persona - all for show. The irony is that this type of wealth is tacky and so will never be accepted by the old money. It tries too hard. From this perspective, the car symbolizes that Gatsby will always be an outsider. 

More importantly, the car symbolizes Gatsby's downfall, as the car will crash and kill Myrtle. In the end, Gatsby, for all this wealth, will come to ruin as well. 

Gatsby's Rolls-Royce figures prominently in the novel. Nick first describes it as "gorgeous" with a horn that plays a three-note melody. His description then becomes more detailed:

It was a rich cream color, bright with nickel, swollen here and there in its monstrous length . . . and terraced with a labyrinth of windshields that mirrored a dozen suns.

The extravagance of Gatsby's car represents his enormous wealth. However, it suggests not the muted elegance of "old money," but instead the lavish, gaudy excess of "new money." Gatsby's car symbolizes his place in society; he has money, but he will never be accepted in Daisy's world of old family names and inherited wealth. Tom alludes to this distinction when he refers to Gatsby's car as a "circus wagon."