The recent changes which require grandparents' birth certificates are because of changes to British Citizenship which took effect on 1 Jan 1983.
Prior to then, being born in the UK was sufficient for you to be a British citizen, so if you had a UK birth certificate, that's the end of the conversation. If you didn't, you obviously could still be a British citizen by a variety of other routes including naturalisation, your father's citizenship, etc, etc, but you'll usually have the paperwork for this.
After 1 Jan 1983, being born in the UK isn't enough. The standard route to UK citizenship is to be born in the UK and one of your parents also being a UK citizen (or "settled", which has a complex definition). Hence the need for grandparents' birth certificates, although I can't quite see why you need all four of them, because if you're both born in the UK post-1983 and your children are born in the UK, I think (I am not a lawyer, etc) that it's sufficient for one grandparent to be a UK citizen.
This is becoming an issue because now, a large proportion of children applying for their first passport have both parents born after 1/1/83, and therefore the child's claim to a UK passport requires one or more of the grandparents to be UK citizens.
See here for the gory details.