Private Member Bills are basically bills introduced in the parliament by a member who is not part of the government. Bills introduced by the government are explicitly called Government Bills.
What's the big deal about Private Member Bills?
Well, nothing really. The fact that they don't see the day of light is the big deal about Private Member Bills or PMBs. In a normal 5 year parliament session in India, about 300 to 350 PMBs are introduced, and hardly a handful come up for discussion and barely any Bill becomes a law.
Why doesn't a PMB become a law?
Its kinda common sense. How can the party in power support an idea introduced by someone not in government? Wouldn't it look bad? But what it if was genuinely a good idea?
Well in that case, the government or the minister who's purview this bill falls under will raise and try to convince the member to withdraw the propose. The minister or the government would then say that they would introduce this bill from the government's side and that would have higher chance of becoming a law. Ofcourse the gullible member does withdraw the bill and the government forgets that it had made a promise. Hence it never sees the light of day.
It might not come as a surprise that no PMB has become a law since 1970. There were a few Bills that either passed in Lok sabha or Rajya Sabha, but none of them have crisened as law of the land. The last PMB bill to pass either of the house was in 2014 introduced by Tiruchi Siva. It was the Rights of Transgender Persons Bill, 2014. It was passed in the Rajya Sabha. You can find the bill here.
Here's an interesting insight into how Private Member Bills perform. Its a well written article on Money Control.