The physical meaning of the entanglement of two identical `two-level' atomic dipole oscillators is investigated. Using Schrödinger's equation, the development of entanglement from an initial product state in which one atom is in the upper state and the other in the lower state is exhibited. Examination of the correlation of the oscillations shows that complete entanglement leads to full phase correlation of unknown absolute phase. This property serves to explain the physical meaning of entanglement for the class of systems considered and the results of measurements conducted on them, without resort to the `action at a distance' concept associated with the Einstein-Podolsky-Rosen paradox. A recent experiment in which such entanglement was produced and cited as an illustration of the paradox is analysed and explained by the present theory. It is shown that the Bell inequalities, unlike in experiments on other entangled states, cannot in principle be tested in this type of experiment.