Translation:My car is big.
My guess is that if you want to say "I have a big car", you'd have to say "watashi wa ookii kuruma ga arimasu." For "there is a big car" you'd just say "ookii kuruma ga arimasu" and the rest would be understood from the context, like if you were counting things you possess, it would still mean "I have a big car". I'm not a native speaker though so can't assure you this is right.
Particles would play a part in that, I would assume. Using が would indicate cars are already a part of the conversation or that you are the topic. If the sentence used は it would be introducing cars as the topic. So 大きい車があります- (Speaking of me,) there is (I have) a big car. And 大きい車はあります (Speaking of) big cars; there is one.
It's the kanji for car, vehicle or wheel(s), so it could very well be old, but the meaning has changed over time. Even the English word "car" had a different meaning 150 years ago. But why couldn't new signs be created also? They have evolved many times in the past, according to necessity, so why not now also?