An election slate is typically a list of candidates for public office presented by a party or organization. This can also refer to a single piece of black stone used as a writing surface.
You might hear about a slate of candidates running for city council, and that means all the people from one group who are trying to get elected. The word 'slate' here refers to a list. Think of it like a menu at a restaurant - just as they have a list of dishes available, a party or organization has a slate of people they're supporting for office.
How common is "slate"?
Word slate is considered uncommon in modern English. It has a balanced usage among all categories: speech, fiction, newspapers and academic texts.
Definitions
noun
(countable) A flake or piece of certain types of stone that tend to cleave into thin layers.
A generally rectangular piece, originally of certain types of stone and now of other materials, often in a frame, used for writing on with a thin rod of the same or another stone (a slate pencil) or with chalk; a small chalkboard.
Synonym of tablet computer (“a hand-held portable computer in the form of a tablet with a touch screen interface”).
Synonym of clapperboard (“a device consisting of a board on which information about a film being recorded is noted, and a hinged piece which is brought down on the board with a clap at the start and end of each take of the film; it is used to synchronize picture and sound during editing”).
A record, for example, of money owed.
Example: Put it on my slate—I’ll pay you next week.
A range of things; also, a schedule.
A collection of films released during a certain period, either from one studio or from a certain film industry (such as Hollywood) as a whole.
A group or list of candidates for appointment or election to an office; also, a group of candidates or electors with affiliated political views.
(uncountable, geology) A fine-grained homogeneous sedimentary rock composed of clay or volcanic ash which has been metamorphosed so that it cleaves easily into thin layers.