A security envelope is an envelope that is designed in such a way that it is difficult or impossible to inadvertently (or advertently) read the text of a letter through the envelope. The most common way to do this is to print a lined pattern on the inside of the envelope, that will obscure the writing. As far as I can tell, there is little premium in price for security envelopes versus normal envelopes, and no reason not to use security envelopes.
It also seems a little ironic to me that in a world where electronic security involves such things as number theory and computers that can crunch 128 bit numbers...the physical security of data depends on an envelope having printed squiggles on it. But then, like most security, its purpose is keeping honest people honest.