Hi and welcome to TravelPunk... now let's see if we can satisify some of your hostel-related curiosity.
First, in regards to double rooms: Check the hostel web site and booking information carefully. Many hostels have rooms with a double bed, where you'll pay a single price for two people. If you're unsure of their pricing scheme, call the place or send them an email to find out what's what.
Second, in regards to value compared to hotels: For couples or groups, sometimes hotels do work out to be cheaper than a hostel, especially in cities where hostels are expensive (Dublin comes to mind...) or off-season hotels can be found on the super-cheap. However, other things can bump up hotel costs like taxes, "hospitality charges" (i.e. more taxes), and other fees that aren't mentioned until you get your bill. It all depends on the city/country, of course.
Finally, the overall appeal of hostels: Certainly, we'd all love the luxury of a full-service hotel if we could afford it. However, some of us *can* afford it, but go the hostel route not just for the economy, but for the backpacker community of it all. Sharing a bathroom or a kitchen or lounge may not be everyone's cup of tea, but for many others, it's a great way to meet new people, share some common ground, and simply be more social. You meet people from all over the world, and you can get insights into towns from long-term residents that no hotel concierge would let you in on... It's just a different style of travel. You definitely give up privacy and peace and quiet, but you gain a whole bunch of other stuff.
If you're still unsure, you might want to give a hostel a try, just for a couple of nights, or perhaps one domestically just to see if it's the right "scene" for you and your wife. Or, you can find smaller, more B&B-like hostels (depends where you're going) that are kind of a cross between backpacker central and a private home.