My parents were Owen and Constance Papineau.Could I have had different parents?Surely not.A Person with different parents would not have been me.So it is necessary that David Papineau's parents were Owen and Constance Papineau.But this statement is surely not a priori.You need evidence to know who my parents were.It's not something you can find out just by thinking.So that's one emample of an a posteriori necessity.
Here is another.Hydrogen is made of atoms containing one electron.This is surely necessary too.Hydrogen couldn't have had a differentatomic structure.Anything with a different atomic structure would't be hydrogen.But this statement too is obviously a posteriori.Physicists didn't figure out the structure of hydrogen by sitting in an armchair.They needed to perform a great number of detailed experiments and observations.
Perhaps the most obvious examples of a posteriori necessities are simple identities involving proper names.Marilyn Monroe is Norma Jeane Baker.This again is necessary.Marilyn Monroe couldn't not have been Norma Jeane Baker.That would require her somehow not to have been herself,which would be absurd.But Marilyn Monroe is Norma Jeane Bakers not a priori.Somebody could understand this statement perfectly well and yet not know it is true.(Imagine someone who grew up with Norma Jeane but lost touch with her,and had heard of Marilyn Monroe but not seen any of the films.)