A double envelope means that your invitation suite will be protected by an outer envelope. 

This is especaially recommended when using envelope liners or wax seals on the inner envelope so that the liner doesn't get torn when guests open their invitation and the seals do not get damaged in the mail.

You will need addressing (guest's names (formal- ex: Mr. and Mrs. John Smith) and addresses on the front and your return address on the back ) for the outer envelopes and names of guests (less formal- ex: John and Jane) for the inner envelopes.