public Vector4[] tangents { get; set; }

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 used to flip the binormal if needed.

Unity calculates the other surface vector (binormal) by taking a cross product between the normal and the tangent, and multiplying the result by tangent.w. Therefore, 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 Mesh.normals or using Mesh.RecalculateNormals.

Note: To make changes to the Mesh.tangents, it is important to copy the tangents from the Mesh. Once the Mesh.tangents have been copied and changed, the Mesh.tangents can be reassigned back to the Mesh.