A CTO owns the technology decisions that are expensive to reverse. Not the day to day code, and not the sprint board: the choices that set the cost of everything you build for the next two or three years.
In practice that is four things. Deciding the architecture and the platform. Deciding what the engineering team should look like and who to hire. Deciding what to build in-house and what to buy. And translating between the technical reality and the commercial one for the CEO, the board and investors.
A good CTO spends more time saying no than yes. Most technical failures at small companies are not bad code. They are the right solution applied to a problem the company does not have yet.