An underwriter is the person in charge of accepting a risk. Behind every insurance policy, there is an underwriter that had to say yes to the policy and found the exposure to be within their risk tolerances.
The term underwriter came from the early days of shipping, specifically in London england. Voyages to new worlds were expensive, so captains sometimes needed to look for investors.
The captain would display a manifest in a public place, like the coffee shop run by a gentleman named Lloyd, and investors would assess the risks of the voyage. If they were okay with the risk, they would write their name literally under the voyage on the manifest to share in the cost of the voyage. In case of disaster, they would be out their investment. But if the voyage was a success, they would also share the rewards! These investors became known as Underwriters.