The direction/consultation axis is the degree to which you take input from your subordinates in decision-making and on other questions impacting the running of your department.
Highly directive managers do their own analysis, make decisions on their own, and tell employees how things are going to be.
Consultative managers listen to people's ideas and analysis, hear their thoughts about how to proceed in various circumstances, and take their views into account.
This is not to say that the boss relinquishes control over decision-making or is obliged to accept the suggestions of others; the person responsible to the higher-ups is always the one who has the final say. But a consultative manager hears what others ...