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A COO is in charge of daily operations of the company and reports to the CEO. A famous COO would be Sheryl Sandberg at Facebook.

Daily operations as in "make sure the site is not down and make sure everybody in the office is doing something productive" ?

the COO varies based of the need of the CEO and their working relationship

This talk/interview of Keith Rabois is great when it comes to talking about what a COO does: http://firstround.com/article/Keith-Rabois-on-the-role-of-a-...