The tangents of the mesh.
Tangents are mostly used in bump-mapped shaders. A tangent is a unit length vector that follows mesh surface along horizontal (U) texture direction. Tangents in Unity are represented as Vector4, with x,y,z components defining the vector, and w used to flip the binormal if needed.
Unity calculates the other surface vector (binormal) by taking a cross product between normal and tangent, and multiplying result by tangent.w. Thus w should always be 1 or -1.
You should calculate tangents yourself if you plan to use bump-mapped shaders on the mesh. Assign tangents after assigning normals or using RecalculateNormals.