Essays are designs for stamps that don't get issued. If they are issued, these designs are then called Proofs. Essays come in two main types- design essays and production essays. Design essays are artist's productions for proposed stamps. These designs may come as a result of an authorized postal authority stamp production process where artist's designs are produced and modified based on artistic production and political considerations. Design essays are also produced on spec- an artist or designer has an idea for a stamp and produces an essay in the hopes of selling it to a postal authority. Design essays also include paper essays. In the 1860's, the United States post office toyed with the idea of printing stamps on goldbeaters skin, a very thin glassine like paper from which the printed design floats away when these stamps are soaked. This plan was to deter potential reusers of stamps. The grills of 1867 produced many essays as printers experimented with the right grill designs for printing efficacy. Indeed there is a grilled all over essay that looks suspiciously like US#79 and is often offered as such. Production essays are printed stamps that are changed after they go to the press and then are not issued for political or artistic reasons. Because they were issued in limited quantities, the Legends of the West sheets (#2170) are stamp issues. But when they were discovered after printing to have a design flaw there was serious discussion about not selling any at all. Had they not been sold officially over the post office counter (as we say) they technically would have been essays.
United States collectors are fortunate. The Essays section in the Scott Specialized catalog is one of the most comprehensive Essays listings of any country. Take a look. You'll see many interesting essays of stamps you know that list for only a few dollars. But, try to find them. When you do they make a very interesting addition to a collection.