Cover is used by stamp collectors to describe any envelope that has been through the mail. An envelope with postage on it is also referred to as "entire" whether it is used or unused, but more usually applied to postal stationery. Any section of an envelope with the stamps applied to it is called a 'piece.'
An Advertising Cover is any envelope with postage affixed that has been through the postal system with advertising printed on it. In today's terms it would be called junk mail.
Back in the day when a visit from the postman was an exciting event a creative way to have a piece of mail make a bigger impression was to dress up the front and back of envelopes with detailed and showy designs. Most businesses who designed these left us with a small peek of the society, commerce, and a little blueprint of that period. Today's collectors cherish them, and while some can be costly, most are inexpensive. An example of how one era's trash is another's treasure. Many philatelics specialize in a specific type of Advertising Cover and there are a great many out there to choose from!
The origins of Advertising Cover could readily be related to the market driven economy of the United States. It was only a matter of time that as soon as the first person had the idea of putting some type of advertising on his business envelopes that others would soon follow suit, and as production methods improved and became less expensive, the style of advertising would naturally tend towards more eye-catching
The predecessors of the Advertising Covers are obviously illustrated trade cards, business cards, and illustrated stationery of the early part of the 19th century. Advertising covers would have most likely developed earlier, had envelopes been widely used, but the expensive "per page" postal rates in the US prior to the 1840's made the use of envelopes an impractical luxury. When the US - following the lead of Great Britain - began using lower, weight-based postal rates, envelopes immediately gained popularity. Notably, the first envelope-making machine was patented in the US in 1848.
John R. Biddle in the 1970's assembled what still may be the most varied and extensive collection to date of the advertising covers of the US and Canada. He has published the highlights of his collections as The American Illustrated Cover Catalog.