Back in the good old days, when the term "cut-and-paste" actually involved scissors, typewriters only had one font.
Using the typewriter to emphasise things, you really only had Bold (i.e. typing a letter twice in the same position), and Underline (i.e. typing the underscore character "on top of" a letter).
So in order to add larger headings one would have to implement alternate technology.
Letraset was that alternate technology. Decades before the latest breakthroughs in WYSIWYG word processing, Letraset was providing a huge array of fonts, bullets, borders and wingdings, all in the comfort of your own home.
Letraset sheets were basically sheets of plastic with a whole series of transfers affixed to one side. You would line up the particular letter (or wingding, whatever) where you wanted it on the page, and then rub vigorously on the back of the sheet with a ball point pen. You had to be careful that you rubbed over the whole letter, otherwise the letter (which was ultra-thin) could crack.
Letraset was also often used to draw graphs - I suspect most PhD theses submitted in the 1970s would have used Letraset in their manuscripts.
Now, I'm not all that old, but the reason I remember Letraset fondly, is that a spin-off product from Letraset were "Letraset scenes" (I can't remember the actual name of the product, unfortunately).
Aimed at children, these "Letraset scenes" would consist of a three-panel cardboard cartoon background, and a sheet full of licensed artwork, usually Disney characters, as well as vehicles, trees etc.
Entire afternoons could be spent transferring pictures of Mickey and Minnie into your own Disney story!
And of course, when you had used up all your Disney sheets, you could always coax your father to give you all his left-over sheets of letters and wingdings - the ones with all of the "z"s and "x"s on them :-)
Those were the days, and there will never again be the like...
Postscript: I was delighted to find out that there is a www.letraset.com which, judging from the corporate graphics, is certainly the same company.