COO, a chameleon in the company
First, let's make one thing clear: COO is not CEO's "go there, do that" boy." When you see a company where the CEO is seeing his COO just as an assistant, you may be sure something is very wrong with that company.
Since the CEO role is to think about the strategy and her COO should make it a reality, it may seem that chief operating officer is just another employee, a bit higer on the corporate ladder but still an employee as any other. And that's far from the truth.
Second, there is no definition of what the exact COO role is. There is a good explanation for that: A COO must solve a broad range or problems and think about many things.
Thus, the role differs from company to company but one thing stays the same: there is no efficient company without a good COO.
The true role of a COO is to be a chameleon in the company. There are usual daily stuff to take care of: production, supplier relations, coordination of various departments...
The point it, your COO must have an engineering mind because almost every problem you put on the table is something new and different and it demands a person who like different and unpredictable jobs.
But, your COO must also pay attention to laws and regulation, have daily meetings with the top management, take care about other companies in the field, share visions with the CEO, give input about new hiring...
In a sense, the role of your COO is similar to the role of a top hotel's consigliere: Make it happen. The only request: legally.
Taking all that into account, you may see that the COO is formally the second in command, but in many ways she's The One that makes it happen. Without good COO there's no smooth business, no matter how good your business plans may be. That's why they are sometimes seen more as an extension of the CEO than just another top manager.
Since your COO works on so many different field, there may come time when someone will say "We know you're working hard, but - what exactly?" Then you should explain COO's role in the company because it is too important to just answer "Bringing our vision to life."
Explain in plain English what does it mean to take care about people, suppliers, orders, regulations, board, prices, marketing... Every day.
Now, you'll probably ask when's the right time to hire a COO.
The right answer is: now. From startup to big company, you need some kind of glue that can hold all departments and various managers together, while staying on CEO's course. If you don't have a COO, you still have to manage all those different parts of your company and take care that production is running smootly.
In other words, you already have a COO, it's just that she's dispersed among several person. But it's much better and much more effective to establish a role of a COO and let other do what they do best.