The inside envelope is typically used for more formal weddings and events. An additional benefit to the inside envelope is that you can put the name(s) of those invited on the envelope to make it clear to the recipient (for example if a guest is invited, you can write "the name of the person invited and guest" on the inside envelope vs. on the outside that you stamp.

It is perfectly acceptable not to use them.

CWC answered above for what the inside envelope is used for in wedding invitations today, but originally, the invitation was placed inside two envelopes because mail was delivered by hand. If the invitation had to be carried through rain, mud, on horseback, etc. then once it arrived at its destination, the invitation could be removed from the outer envelope and the clean inner envelope would be placed on a tray and delivered by a servant to the intended receiver.
As far as whether it's tacky to not have an outer and inner, there are more issues involved than that. If you are trying to go by strict etiquette, then yes, an outer and inner envelope is required. If you are concerned about waste and are trying to have a "green" wedding, by all means forego the inner envelope. And really, do you want to invite someone to your wedding who would think you were "tacky" just because you didn't enclose an inner envelope? It's your day, do it your way!