A set meal provided at a reduced price.
The phrase 'blue plate special' isn't widely known here in the UK. In fact, until questions were asked about it at our bulletin board, I'd not come across it before. It is American and originated there around the start of the 20th century.
A common expression in the USA, but largely unknown elsewhere.
Considering that the expression has been in common use in the USA for a century or so, the usual US reference sources have little to say about it. A useful first port of call when researching American colloquial expressions is Lighter's Historical Dictionary of American Slang, but the term isn't listed there. Webster's Dictionary does help out by defining 'blue plate' as:
1. A restaurant dinner plate divided into compartments for serving several kinds of food as a single order.
2. A main course (as of meat and vegetable) served as a single menu item.
Webster's doesn't cite an origin but there seems little reason to look further than the colour for the derivation of the phrase - blue plate specials were served on blue plates, usually divided into sections for meat, potatoes etc. Nor does there seem to have been anything especially significant about the colour. Cobalt-blue has been commonly used as a pigment for crockery since the Chinese developed the Willow Pattern design in the 17th century. The number of pieces of blue and white pottery that gardeners find is evidence of its past popularity in both the UK and USA.
Blue plate specials don't invoke images of what gourmets call 'fine dining'; we are more in the region here of the establishments that Singer and Zaret wrote about in the song 'One Meat Ball', with its sad lyric 'you get no bread with one meat ball'.
The earliest citation of the phrase that I've found is in this advert for the Young Women's Christian Association, printed in the Illinois newspaper The Decatur Daily Review, September 1924.
The food writer Daniel Rogov claims that 'blue plate special' was first used on 22 October 1892, on a menu of a Fred Harvey restaurant on the Atchison, Topeka, and Santa Fe Railroad. I've not seen a copy of that menu and so can't confirm Rogov's assertion, although the use of so specific a date would seem odd if it weren't taken from an actual menu.