A plate (i.e., photographic plate) is a pane of glass coated with the photographic chemicals necessary for taking a photograph, an alternative to the use of film. Photographic plates have been used in astronomy since the late 1800s, but such photography has been replaced by the use of electronic sensors such as CCDs, introduced in the late 1900s. Film has been used as well, but plates have the advantage of stability of their size: no stretching or shrinking. One astrometry practice is literally measuring physical distances between imaged objects on a plate, so this stability is relevant.
Surveys have resulted in collections of plates, which have been used for years to create catalogs of various kinds of objects, often with more than one plate for each field, taken with various filters. (Note that such collections may include film as well, not sometimes referring to the film as plates.) Example collections are the POSS plates from the Palomar Observatory Sky Survey (POSS), and the ESO plates from the UK Schmidt Survey. More recent surveys like the Sloan Digital Sky Survey (SDSS), that do not use photography produce data sets used similarly. Plates as old as a century retain value by offering data regarding peculiar velocity, visual binaries, variable stars, supernovae and other transient phenomena, and earlier positions of solar system objects.
The term plate has other uses: in some situations a lens is referred to as a plate.