Pinjar was a Punjabi novel written by Amirita Pritam and a Hindi film based on that novel.
In Punjabi, Pinjar means Skeleton. So as far as one can guess, the meaning of Pinjar, the novel and movie should be skeleton only, but an interesting thing is that in Hindi, the language in which the film was made, a cage is called a Pinjara, or sometimes, Pinjar. Also, going by Pinjara, one may call someone kept inside a cage Pinjar.
So, this one thing that fascinates me the most about the name of the movie is that even if you do not get the name right, the one from Punjabi, the meaning of the title is not completely lost and you get a somewhat similar idea of a caged bird.