ingles, I find that irksome too but I think he's trying to be a bit facetious. I could be wrong though, it's hard to tell with Scott Mills.
ChippingIn, the apostrophe is used to show contraction (where a letter/letters have been removed) e.g. can't, I'm, They're, it's.....
It is also used to show possession: Betty's cake, my Dad's car, the cat's whiskers, London's streets..... except where the noun is 'it' (the cat cleaned its whiskers).
Where the noun is a plural, the apostrophe comes after the 's' e.g. the boys' shirts. One that sometimes catches people out is plural and possessive of 'baby' and 'lady':
The babies are crying (more than one baby)
The baby's cot (one baby, possessive)
The babies' cots (more than one baby, possessive)
Where the apostrophe is NOT used is to show a plural, and this is the usage which riles a lot of pedants. It is sometimes known as the greengrocer's apostrophe, thanks to its appearance on greengrocer's signs (apple's, orange's etc...)
Hope that helps!
Just thought of another annoying one: whose and who's.