A mujtahid is a jurist qualified to derive rulings directly from the sources rather than following the settled positions of a school, and the office is far more consequential in Twelver Shia usage than in Sunni.
Independent reasoning
The mujtahid is competent to exercise ijtihad, the independent effort of deriving legal rulings from the Quran, the practice of the Prophet, consensus and reasoning, rather than merely applying the established rulings of a school, which is the ordinary work of most jurists. This requires the highest level of legal training and mastery of the sources and the methods, and the classical qualifications for it are demanding, so that the mujtahid stands above the ordinary jurist who follows an inherited position.
The Shia difference
In Sunni Islam the scope for fresh ijtihad narrowed as the schools of law matured, and most Sunnis follow the settled positions of a school, so the living mujtahid is less central. In Twelver Shia Islam, by contrast, the office is fundamental: every believer not himself qualified must follow a living mujtahid of the highest rank in matters of practice, and the most senior mujtahids, recognised as sources of emulation, hold great religious authority and, in the modern Iranian doctrine of the guardianship of the jurist, potentially political authority as well. The office of the mujtahid is thus the point at which the Sunni and Shia understandings of religious authority diverge most sharply, the one resting on the schools and their accumulated law, the other on the living jurist qualified to reason from the sources.