A confederal system is a mode of government in which a number of smaller states choose to delegate some of their policy making rights to a central body. In this way, the collection of the smaller states can be thought of as a country. A good example of this is the former Soviet Union, which was a conglomeration of a large number of smaller states.
In a confederal system, the smaller states that make up the country have the right to pull out from under the central government at any time. Some of the services that they cede to the central government include foreign affairs, internal security issues, military defense, and in some cases, health services. The states that form the country usually retain their legislative rights, which gives them more power.
A good example of a modern confederal system is the Swiss canton system, in which each of the cantons make most of the policies they need. The United States is not a confederal system, but the Confederate States of America formed one between 1861 and 1865. It is currently a federal system, which is characterized by having a number of states that have considerable independence over their own legislature but follow a strong central government.