Not a tour, but a bundle of airfare, lodging, maybe a car all at wholesale rates
Packaged vacations are a simple concept for powerful savings: you buy your airfare and lodging (sometimes with rental car or train tickets as well) together at a price much lower than you could get any of those big-ticket travel items separately.
A vacation package is not an escorted tour, where they shuttle you around Europe in a hermetically sealed bus bubble of Americanism.
With a packaged vacation, your trip is entirely your own—you just don't have to book everything (airfare, hotels, maybe rental car or sightseeing) independently. You get some combination of those big-ticket items all at once and for less (ideally) than you'd pay if you tried to book them separately.
Packages tend to last for a "week" (which might be anything from four to seven nights), and include round-trip airfare, your lodgings, daily breakfast, and sometimes transfers from the airport to the hotel and back. (Some versions also include a rental car or train tickets or rail pass.)
How packages save you money
You end up paying less because the packager (usually a tour company, travel agent, or search engine) has agreements to buy up blocks of travel products at whoelsale rates and passes some of these savings along to you. (They keep some, of course; that's their profit.)
A downside to vacation packages
The biggest drawback to a vacation package is that most of the hotels they offer for you to choose from tend to be the huge, cookie-cutter international chains or bland "tourist class" properties, in many cases at the edge of the city center, generally near the train station (ugh!).
Sure, the price is great for that sort of four-star hotel, booking these big ticket items all at once can be convenient, and it saves money over buying the airfare and that hotel separately. However, with a bit of research—and the tools on this site—you can find an even lower airfare and book yourself into an even cheaper, more characterful little pensione in the heart of the historic district.
(I should point out that Go-Today.com has actually started finding a few charming hotels and B&Bs in historic or interesting parts of town on a few of its packages. This is an encouraging development.)
The best vacation packagers
Besides the companies listed below (which really do tend to be the cheapest by a long shot), another great place to look for package tours is from the "Vacations" or "Holidays" subsidiaries of the major airlines themselves, though you should know that some of the European carriers sell packages that are far from bargains.