A CTO is just a title for a leader with sufficient technical experience to help guide the company through technical challenges and to represent the technical interests of the company.
When looking for a CTO here are some of the attributes I think are important:
- Is approachable by both technical and non-technical members of the team
- Can get up to speed on the company goal quickly and can ask relevant questions about the trajectory of the company towards that goal
- Can articulate where the tech team needs to be in three years time
- Can get employees excited by company goals (often by adding a tech slant)
- Talks positively about their team and individuals within the team
- Finds opportunities in changing landscapes (internal and external)
- Challenges employees to think deeply on problems
- Pushes for time spent thinking about and acting on tech debt
- Shares interesting ideas and thoughts both internally and externally
There is a bit more to it than that, but other attributes are specific to the industry or company the CTO would be working in.
When I take on projects as an interim CTO, I put things in place to help a permanent CTO meet these attributes.