Final answer:
A certificate of authority permits an insurance company to conduct business in a specific state, such as Texas, and is essential for legal operations within that state.
Step-by-step explanation:
A certificate of authority is an official document that permits an insurance company to transact business in a particular state. Therefore, the correct answer to what a certificate of authority does is option 4) permits an insurance company to transact business in Texas. This document is essential as it provides the legal right for an insurance company to operate within the state's jurisdiction and offer its products and services to the residents. It is not related to giving an agent individual authority, permitting an agent to solicit insurance in Texas, or allowing a deceased agent's relative to act as an agent.