What is the meaning of [For ever and a day]

Indefinitely.

Of course, for ever and a day is an dramatic construct with no literal meaning – for ever is for ever, we can’t add days to it. This form of dramatic emphasis has been used many times, a recent example being The Beatles’ song ‘Eight Days a Week’.

Shakespeare coined this and used it in The Taming of the Shrew, 1596:

BIONDELLO I cannot tell; expect they are busied about a
counterfeit assurance: take you assurance of her,
‘cum privilegio ad imprimendum solum:’ to the
church; take the priest, clerk, and some sufficient
honest witnesses: If this be not that you look for,
I have no more to say, But bid Bianca farewell for
ever and a day.