I'll assume by "President" you mean the President of the United States, though portions of this answer can be applied to Presidents of other countries or other leadership positions.
The President does seek the advice and council of his Cabinet for a number of reasons, as Cabinet members administer the departments and agencies for which he or she oversees. Cabinet members are nominated by the President, they need approval of Congress to serve.
The Cabinet Members not only oversee various functions of the government that the President presides over, but manages various government responses to emerging crises and concerns to our nation.
For example, President Obama is currently considering the next best course of action in Afghanistan. The President may decide to send many more troops to Afghanistan. This is not an easy decision to make, so he seeks the advice and counsel of key cabinet officials to make this decision. Some feel this is too big of a cost, as it will put more soldiers at risk and cost the federal government a hefty sum during a time of domestic economic strain. Others feel strongly that our nation's security depends on sending more troops to Afghanistan, as those that waged or supported the 9/11 attacks see the U.S.A. as their enemy and will strike on U.S. soil once again.
To make his decision, he'll seek advice and help from those who lead our Nation's efforts in key ways.
He'll seek input from Defense Secretary Gates, who leads our military strategy in Afghanistan, and receives reports General McChrystal, and others serving in Afghanistan and the overall region.
He'll seek similar input from our chief diplomat, Secretary of State Hillary Clinton, who oversees our nation's diplomatic corps and have a full understanding of the current scenarios potential decisions will have on the region - in Pakistan as well. Gaining input from our ambassadors and envoys to the region is crucial. Certainly the recent elections have created complicated diplomatic scenarios to weigh and balance, and she recently visited the area.
Vice President Joe Biden is also a top adviser to the President on most everything he's considering. Given the Vice President's previous role as the chair of the U.S. Senate Foreign Relations committee will certainly make him a crucial adviser to the President.
Ambassador to the UN Susan Rice also has cabinet status, and working with her advice regarding potential UN involvement will probably be a consideration.
He'd likely consult OMB director Peter Orszag to help gauge the price tag of his potential options, as choices to send more troops will impact the federal budget.
His chief of staff likely weighs in on such decisions too, and he has Cabinet level status.
Plus, he'll seek the opinions and advice on courses of action from key leaders in Congress, who not only have their own diplomatic role abroad, they also have constitutional power to approve the budget for our federal government as well as upon decisions of war.
I've linked to the official White House page on the cabinet to help.
For what it's worth, entire books have been written about how and why our Presidents make the decisions that he makes. See Doris Kearns Goodwin's NO ORDINARY TIME to learn about FDR's role in WWII, as one example.
See this NY Times article for some incite about how the President's cabinet may be weighing in on the President's decision regarding future strategy in Afghanistan: http://www.nytimes.com/2009/10/13/world/13cabinet.html
Hopefully any President will make the most informed decisions that he/she can, with the most information possible, by consulting key advisers who represent as many useful or potentially successful options as possible. He's likely chosen his cabinet to account for the type of advice he or she can give, and chose them because of their abilities to recommend strategies and tactics to the problems we're facing as a country.
While the decisions a President makes certainly creates debate and controversy for the toughest ones, the President typically has to make them because nobody else has created a solution to these tough problems.
As our current President has said on many occasions, he typically only gets to make the decisions that nobody else has solved, and they typically are the toughest ones.
Also, for what it's worth, this administration has made a sincere effort to increase the amount of citizen input for decision-making: http://www.whitehouse.gov/blog/Enhancing-Citizen-Participation-in-Decision-Making
Source(s):
http://www.amazon.com/No-Ordinary-Time-Franklin-Roosevelt/dp/0684804484/ref=sr_1_3?ie=UTF8&s=books&qid=1257282664&sr=1-3
http://www.whitehouse.gov/administration/cabinet
http://www.whitehouse.gov/blog/Enhancing-Citizen-Participation-in-Decision-Making
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