Usually, when you hear the term "partnership," it refers to a general partnership -- that is, one where all partners participate to some extent in the day-to-day management of the business. Limited partnerships are very different from general partnerships, and are usually set up by companies that invest money in other businesses or real estate.
While limited partnerships have at least one general partner who controls the company's day-to-day operations and is personally liable for business debts, they also have passive partners called limited partners. Limited partners contribute capital to the business (investment money) but have minimal control over daily business decisions or operations.
In return for giving up management power, a limited partner's personal liability is capped at the amount of his or her investment. In other words, the limited partner's investment can go toward paying off any partnership debts, but the investor's personal assets cannot be touched -- this is called "limited liability." However, a limited partner who starts tinkering with the management of the business can quickly lose limited liability status.
Doing business as a limited partnership can be at least as costly and complicated as doing business as a corporation. For instance, complex securities laws often apply to the sale of limited partnership interests. Consult a lawyer with experience in setting up limited partnerships if you're interested in creating this type of business.
For a thorough explanation of the legal and practical issues involved in forming a business partnership, see Form a Partnership: The Complete Legal Guide, by Ralph Warner & Denis Clifford (Nolo).