The Batmobile is Batman's personal vehicle. He bought it from Lucius Fox for his crime-fighting occupation.
On few occasions, such as in the episode "Driver's Ed", Robin was allowed to use it, but unfortunately, he crashed it and got his license suspended. Then Robin must get a new license. In the scene, it is assumed that Robin is talking to Batman about the crashed Batmobile.
A different variation of it appeared in "Sidekick".
The Batmobile appeared again in "Waffles" on the front cover of a newspaper Robin was reading, which apparently lost a wheel while chasing after the Joker. It has appeared in other episodes later such as in "TV Knight" and "TV Knight 2" in the opening scenes.