In the context of forex auction, it is an exclusive market where only members of the exchange can bid on shares that are short delivered. There are specific windows for the auction market. Exchanges do this to make sure that there is not any conflict of interest.
If you are an individual, you must first be a member of some exchange to participate in the auction market.
For other types of auctions, it depends on who is organizing the auction and what their entry policies are. In certain informal agricultural markets, anyone can bid in an auction. In most cases, anyone can take part in an absolute auction.