Identification of the normal cycle to a closed curve

Question

I'm studying the normal cycles in Morvan's book "Generalized curvatures"; He says that the normal cycle of a domain D bounded by a smooth curve is the current ( i.e the linear continuous functional with compact support ) associated to its unit normal bundle. What i don't get is when he identifies this current to a closed curve by the exponential map : \begin{array}{ccccc} T & : & TU & \to & U \\ & & (x,\eta) & \mapsto & x+\epsilon \eta \end{array} Please help me understand how does he do this identification?