Basically, it means that the author is providing and selling their own copies of their book. Ideally, the author has purchased their copies at wholesale (or below wholesale) cost. The day of the event, the author brings their books to the store. Sometimes the store will ask for copies ahead of time so they can display them, promote the event and even sell some books prior to the event. Once the author brings books to the store, the manager of the store will either scan the books into their store's merchandising system or they will have some other means of tracking the consignment sales.
Traditionally, the split is 60/40, with the author receiving 60 percent of the retail price for each book sold, and the store receiving 40 percent for hosting the event. Some stores have different splits, so always ask about this prior to the event. Sometimes a store will let the author keep 100 percent of the proceeds from the sale of their own books. They just want the author to bring additional customers in the door because those customers will likely purchase something else while they are there and become repeat customers.
The benefit of doing a consignment event is that the author doesn't get socked with any returns if there are unsold copies. The author simply brings those copies home, or the store may keep the books and sell them for the author on a consignment basis after the event, if the event went well.
"But," the author may ask, "how will this help me get my book carried in bookstores nationwide?" Well, initially...it probably won't. There is nothing wrong with swinging for the fences when you first get into the (publishing) game, but every author has to start somewhere. Every author wants bookstore chains, Wal-Mart and Costco to carry their books nationwide on the book's release date. The fact is, a very small percentage of books get that kind of treatment. Bestselling authors with several titles under their belts, celebrity authors and those who are infamous for one reason or other (think Donald Trump) see their books blasted to stores all across the country when they first become available. For the author just starting out with their very first title, they have a long, hard road ahead of them, and consigment events might be some of the very first bookstore events they land.
It's not as bleak as it sounds. Some very successful authors started out this way. The authors of "Chicken Soup for the Soul", for example, engaged in a grass-roots effort to sell their book when it was first released. It wasn't availalbe in every bookstore and supermarket then like it is now. They did speaking engagements wherever they could get them, sold books through beauty shops, and I am sure they have more than one consignment event under their belts. You know the rest of the story. Now there is a whole series of "Chicken Soup" books, and the authors are very, very successful.
Everyone has to start somewhere, and for many authors, this means starting with consignment events at their local independent bookstores.