It depends on a few factors. An airline is not liable for accidents that occur due to "acts of god," that is, unforeseen events of nature that cannot be prevented. Turbulence is a good example of an act of God. The airline cannot always anticipate turbulence, and if a passenger is injured from turbulence while the airline and attendants were vigilant in protecting everyone, the airline will not be held liable.
However, there are instances where one can sue for being seriously injured from turblance. If the flight crew was able to foresee the turbulence (and often they can), but failed to warn passengers to fasten seat belts or otherwise take precautions to protect passengers from injury, the airline might be liable for passenger injuries. Similarly, if the pilot should have been able to predict the turbulence, but failed to do so due to lack of vigilance, the airline could be on the hook for injuries caused by the turbulence. Another example would be flying into a bad storm instead of going around it or above or below, assuming those were available options.
If you were injured on a plane or an airport, or even a train station or bus station please contact us today at 516-222-4000.