Electron microscopy and electron diffraction have been applied to show that the orthorhombic phase in the compound Ba2YCu3O7-δ is responsible for the high superconducting transition temperature. A positive correlation is found between the volume fration of the orthorhombic phase and the superconducting transition temperature. By means of an "in-situ" heating experiment it is found that the orthorhombic phase is formed on cooling from a high temperature tetragonal phase with disordered vacancies. It is suggested that the low temperature tetragonal phase that occurs in the same specimens as the orthorhombic phase also contains an ordered arrangement of vacancies different from that present in the orthorhombic phase. The order-disorder transition associated with the structural vacancies is shown to be reversible, provided there has been no oxygen loss.