Gowns are easy, but why the name mortar?
An 1876 reference in the OED to the building trade: "A board for holding mortar", but more intriguingly, the headgear was referred to by Cuthbert Bede (pseudonym of Edward Bradley) in one of his novels of Oxford life, Adventures of Mr Verdant Green, in 1854: "I don't mind this 'ere mortar board, as he pointed to the academical cap."
Or you could turn to Brewer's Dictionary of Phrase and Fable where you'll find it was a corruption of the French, mortier, the cap worn by the ancient kings of France.
Cut the literary stuff, what does it look like?
"A popular name for the academic or college cap, which consists of a stiffened head-piece surmounted by a square of 'board', the whole being covered with black cloth." (OED) If you are a university chancellor it can be made with black velvet and adorned with gold bullion, lace and tassels.
Were they ever worn in schools?
Yes, in public schools and those that wished they were, like direct-grant and grammar schools, until around the mid-1960s. But usually only on speech days. Gowns were seen more often as they were beloved by crusty old teahers whose excuse was that they kept chalk dust off their suits.
Do either garments feature these days?
Not a lot, certainly not the hats. Unless you are at an America high-school graduation ceremony (save money by making your own from poster board and yarn). Some independent school teachers might don a gown on ceremonial occasions, or to preside over a formal meal, but even they would eschew the mortar board.
Has this put the maufacturers out of business?
Certainly not. What with the continuing growth of the university sector, and the fact that every institution wants to maintain the traditional graduation ceremony. Market leader in the robing trade, Ede and Ravenscroft (established 1689), for example, reports buoyant business, both for hiring and buying.
How much will this frippery cost?
A Bachelor's degree? For you, guv, a snip at pound;30 a day and yours for pound;137. Not the polyester model? That will be pound;300. That terracotta silk suits you, Madam.
So a great future?
Definitely. Unlikely to re-emerge in schools though; but unless tabloid cartoonists break free from their time-warp, they will remain part of our national psyche. A teacher? He's called Sir, and he's a bloke with a gown and a mortar board, innit?