Complex sentence: In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a numerical invariant that represents the number of times that the domain manifold wraps around the range manifold under the mapping.
Split into simpler sentences: In topology, the degree is a numerical invariant that describes a continuous mapping between two compact oriented manifolds of the same dimension. Intuitively, the degree represents the number of times that the domain manifold wraps around the range manifold under the mapping.