Several sites have great articles about Hinamatsuri, if you'd like to know more about this fascinating tradition and how to celebrate it.
The set of dolls -- hina ningyo/ningyou (also called an ohina-sama) -- is a lavish recreation of Japan's Imperial Court in Heian times, at least 1000 years ago. They are celebrating the wedding of a new young Empress, with all the pomp and accessories that you might expect for such an important and happy occasion. The display of a set of dolls is usually decorated with a branch of peach blossoms.
The contents of one of these sets made for Hinamatsuri will vary depending on a number of factors, like the cost and quality of the dolls, the amount of space available for display, and the taste and skill of the artisan who made them. A complete, high quality set of dolls will cost at least $5000, but many sets top the $10,000 mark. But there are options at lower prices.
An inexpensive hina ningyo for a small apartment might be a self-contained box that unfolds into a decorated platform with a gilded screen and the emperor and empress dolls (dairi-sama), and can cost very little ($25 or even less).
A pricey ohina-sama will have a hina-dan (platform covered with red felt) of five to seven levels, with an array of courtiers: from ladies-in-waiting and political ministers to entertainers and cooks. There may be more than 15 dolls, all with their own traditional accessories and positions on the platform. The scene itself will also have accessories: lanterns, the gilded screen, flowers, a small ox cart, a table of traditional snacks, and so on.
Children generally don't play with the dolls, but many do make-believe that the dolls are honored guests in their home, something like a very formal dolls' tea party.
Dolls may be passed down in a family, but they're also likely to be discarded -- sometimes taken to a temple and burned -- when the girl who owned them feels too old to celebrate the holiday.
Up next: info on the dolls and accessories