I’m not sure what the other answers here are talking about, I believe the reason that wind turbine blades are long and thin is to have a high aspect ratio. Wind turbine blades are basically wings, and in aerodynamics at low speeds a high aspect ratio, or a long and thin wing, will produce less drag for a given amount of lift then a lower aspect ratio, or a short and wide wing. On wind turbines, drag is a loss, as they are driven by lift, so minimizing drag by having a very high aspect ratio makes a wind turbine more efficient.
The type of drag that is caused by generating lift is called induced drag, and it is generally inversely proportional with the aspect ratio of the wing. This is also why most subsonic airplanes have long and thin wings. In particular, if you look at gliders and sailplanes, they also have extremely high aspect ratio wings for the same reason.
There are vertical axis wind turbines that use drag to drive the blades, which do have very wide, sail-like blades.
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