I had this role for a number of years at a consultancy.
My role was to try to develop new areas of thought leadership for the company. What new technical areas should we be pushing into? How could they develop into new markets and services? What should we be out in front trying? How can we be part of defining the field we're working in?
Basically I was the person given a lot of autonomy and trust to be "out in front" on these areas, envision where our field/market was going, and begin the process of defining prospective services/offerings we could make. Others might refine or go in a different direction with these.
Also one other thing I did was to work closely with the most important and strategic clients. Some of these we were partnering with to develop new capabilities in the market. Others were just clients with deep pockets doing cutting edge work.
I got the team excited too. I wasn't a manager, but I was a motivator for getting people excited about the possible direction. I was a focus point for lots of ideas generated by the team, and developed a vision that ensured we rowed in the same direction (and said "no" to the ideas that weren't in this direction).
I coordinated with other parts of the company to make all this happen. With the COO/CEO type folks to understand the budgetary constraints. With sales/marketing to understand whether my efforts were paying off. With engineering to figure out how to realize my marketable ideas into products or services.
*One big takeaway from my experience*
At a small company, so much is driven by the mix of personalities. Don't get too hung up on what any particular job definition is, but find the intersection of personal skills and what the company needs to define a role. I've seen people called "CTO" that actually do slightly different than what I've listed above, because the mix of personalities and type of company dictated a different breakdown of roles. So small companies, these role definitions can be fluid, and you need to explore what the right thing is for you/ your company.