A benrishi is a Japanese lawyer who specializes in, and is only permitted to practice, patent law.
Japan's patent system is somewhat different than that of the United States. In America, a person with a technical background and no legal training can take the patent bar examination and become a "patent agent," allowing them to draft patents for submission to the U.S. Patent and Trademark Office. An attorney with a technical background and law school education can also take the patent bar; if they pass, they become a full-fledged "patent attorney," and are able to file patents and argue patent cases in court.
In Japan, benrishi are best conceptualized as a subset of attorneys (bengoshi). Benrishi are able to file patents and argue patent cases in court, which makes them more powerful, in a sense, than American patent agents. But benrishi are less powerful in another sense: bengoshi are permitted to file patents without obtaining a separate patent qualification (and without the accompanying requirement for a technical degree). So, rather than maintaining a separate turf from garden-variety lawyers, benrishi are specialists, allowed to do most anything within their own narrow field of law, and open to competition from bengoshi every step of the way.