  It is known that the noncommutativity of D-brane coordinate is responsible
for describing the higher-dimensional D-branes in terms of more fundamental
ones such as D-particles or D-instantons, while considering a noncommutative
torus as a target space is conjectured to be equivalent to introducing the
background antisymmetric tensor field in matrix models. In the present paper we
clarify the dual nature of both descriptions. Namely the noncommutativity of
conjugate momenta of the D-brane coordinates realizes the target space
structure, whereas noncommutativity of the coordinates themselves realizes
world volume structure. We explicitly construct a boundary state for the
Dirichlet boundary condition where the string boundary is adhered to the
D-brane on the noncommutative torus. There are non-trivial relations between
the parameters appeared in the algebra of the coordinates and that of the
momenta.
