'Vital statistics' are births, marriages and deaths. You may also hear "vital records" or "BMDs" and they are often kept by civil registration. Civil registration began in this country (UK) in 1837 and still continues (Sweden began theirs in 1631). This is what provides birth, marriage and death certificates. I wrote about certificates in my A-Z Challenge 2012 post here, Back then in 2012, FreeBMD had transcribed over 214 million records (of references you need to order a certificate). Two years later, and it is over 302 million.
In 1837, some people were wary of registering vital events in their lives, in case they were going to be taxed (well, that's not such a stupid idea; there had already been weird things like hair powder tax, window tax, and dice tax). In fact, it was not until 1875 that it became compulsory to register, and unfortunately some errors have crept into the registers over the years, which is why you may find some difficulty occasionally when searching.
And it's the searching where this years 'back to genealogy basics' comes in. When you are looking for an ancestor, don't expect to find the exact village in civil registration indexes. Villages, towns and cities were organised into registration districts, so for instance the village of South Pool is in the Kingsbridge Registration District. My ancestor wasn't born in Kingsbridge! Don't let that lead you down the wrong path.