The role of a COO (Chief Operating Officer) is not always clear to outsiders. Nor, I would I add, is it always clear to us COO's. It's different from company to company and from time to time.
As a member of the Executive Team, the COO contributes to making decisions on the direction of the company. Figuring out what direction to take and why.
Direction = Vision + Strategy
And for the company to be successful it needs to be capable to pursue that direction.
Success = Direction x Capability
The word "Capability" in the above equation is where the COO has to focus. He/she needs to create and improve the "capability" of the company in order that it can pursue it's objectives effectively.
Digging deeper, capability has two main drivers...
Capability = Competence x Capacity
Competence is how good we are at doing something and it's driven by 4 main factors;
Competence = Communication x Skills x Experience x Information
Capacity however is how fast we are at doing it and it's driven by how many resources we have (money, people, assets) and how productive or efficient we are with those resources.
Capacity = Resources x Efficiency
If the COO is concerned with Capability, then the COO's time by neccessity needs to centre around Communication, Skills, Information, Resources and Efficiency.
That means that COOs tend to think about organisational health, talent, inventory, feedback loops, processes, procedures, controls, systems, planning, reporting and troubleshooting.
So if Success = Direction x Capability
then
Success = (Vision + Strategy) x ((Resources x Efficiency) x (Communication x Experience x Skills x Information))
At least that's the way I understand things, for now.