Let M be a manifold, let nabla be a linear connection on the tangent bundle of M, and let T be a tensor field on M.  Then the covariant derivative of T with respect to nabla is nabla(T) = nabla_{E_i}(T) &t theta^i, where the vector fields E_1, E_2, ..., E_n define a local frame on M with dual coframe theta_1, theta_2, ..., theta_n.  The tensor nabla_{E_i}(T) is the directional covariant derivative of  T with respect to nabla  in the direction of E_i. The definition of the covariant derivative for sections of a vector bundle E -> M and for mixed tensors on E is similar.

This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form CovariantDerivative(...) only after executing the command with(DifferentialGeometry) and with(Tensor) in that order.  It can always be used in the long form DifferentialGeometry:-Tensor:-CovariantDerivative.