Endorsements have been around since humanity started using symbols to represent names or affiliations. It is a mark on an envelope or on a folded and sealed letter that indicates an official mark of propriety. Regardless of the type of endorsement on an envelope, all are meant to represent an official seal or entity of origin.
Technically, any envelope with a stamp on it that gets processed and delivered through the USPS is endorsed. The mark the USPS places across the stamp is an endorsement. It has the date the envelope was received in the post office and the city of origin. When a stamp is not used, the endorsement is the same but also includes the value of the postage. Other USPS endorsements include instructional information stamped directly on the envelope (i.e., Do Not Forward).
Often, organizations will require a sealed endorsed envelope for important documentation to ensure it is coming directly from its place of origin and has not been tampered with (i.e., colleges will request transcripts this way). The endorsement can be in the form of formal letterhead on the outside of the envelope and can also include a stamp on the seal to ensure it is not opened prior to delivery.
Historically, the most recognizable endorsements were wax seals stamped with a signet ring or other personalized seal, a practice still in use today. However, this is used infrequently and more for the sake of tradition rather than any official purpose. Signatures on the outside of an envelope were also considered an endorsement back in a day when such things were not called into question for being fraudulent. Wax seals were most often used by royalty, while signatures were used by other people of importance, such as artists or military personnel.
Well known companies will sometimes allow other organizations to include advertising literature in their endorsed envelopes. Their clients or people on their mailing list are more likely to open a communication from someone they recognize, so other solicitors will pay a fee to be included in an envelope endorsed by a company that already has credibility with its clients. Often these added inserts are included in bills or bank statements.