I'll have the mother's educational level as a good predictor. I think in another generation or so it will be both parents, as childcare arrangements change.
The first people a child talks to are its parents. In the early, vital years, when the brain is geared to learn so much and so quickly, they are its first, primary and possibly only teachers.
So take one reasonably bright child: (and speaking incredibly generally, and not accounting for individual circumstances)
Mum One is educated, has studied, read and talked about lots of subjects over the years, has (mostly) moved cross-country to university, mixed with all those different people, with different specialisms, learned to structure language correctly and professionally, and, crucially, values and likes learning still.
Mum Two left school at 16, having never engaged, works and lives in the same village she was born in, reads a bit, but always the same type of fiction, and watches mostly soaps and light dramas on TV.
Mum One is giving her child an 'advantage' every time she speaks. Her spoken language will be 'better', her vocab generally more broad. She's likely to encourage a greater and earlier appreciation of books and knowledge. She's more likely to able to answer questions. She'll research schools, support homework. She'll also more likely have, or be able to acquire, the skills to teach her own child early maths and literacy.
Effectively, Child One gets 4-5 more years of 'learning-time' than Child Two, and then however many more of more and more-effective support.
It won't change a below-average child into a super-genius or anything like, but between two children equally naturally capable, Child One has a heck of an advantage.
Think about yourselves: When you child was learning to talk, were you talking back? Saying 'yes, DD or DS, that's right', or 'gently correcting pronunciation?' It's automatic, right? Imagine that, all the way through school!