A self-addressed stamped envelope (or just stamped addressed envelope (SAE) in the UK) is often just that: an envelope with the sender's name and address on it, with affixed paid postage and mailed to a company or private individual. Often, SASEs are used when sending for information about products or services.
Companies use SASEs in order to save on postage; a consumer can afford the cost of a stamp and envelope, but the business does not want to pay for the postage on all the letters it sends out.
One of the most common uses is when companies are legally required to send something upon request, such as a "winners list" at the end of a sweepstakes; the company will require a SASE with the request, to avoid paying the postage.