Complex sentence: So spinors are elements of a vector space (often over the complex numbers) together with a representation of the special orthogonal Lie algebra (infinitesimal rotations or infinitesimal Lorentz transformations).
Split into simpler sentences: So spinors are elements of a vector space (often over the complex numbers) together with a representation of the special orthogonal Lie algebra. That is, they transform under infinitesimal orthogonal transformations (such as the infinitesimal rotations or infinitesimal Lorentz transformations).