This style involves the leader including one or more employees in the decision making process (determining what to do and how to do it). However, the leader maintains the final decision making authority. Using this style is not a sign of weakness, rather it is a sign of strength that your employees will respect.
This is normally used when you have part of the information, and your employees have other parts. A leader is not expected to know everything—this is why you employ knowledgeable and skilled people. Using this style is of mutual benefit as it allows them to become part of the team and allows you to make better decisions.