What does a molecule having dipole moment signify?

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Can someone give me a clear picture of it's physical meaning? What does a molecule having dipole moment signify? All the explanations I've seen are very hazy.
 
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Basically you can think of the dipole moment as representing how off-center the positive charge in an object is compared to the negative charge. So if you have a molecule with some extra positive charge on one end and some extra negative charge on the other end, it will have a large dipole moment. (That would happen if the latter end attracts the molecule's electrons more than the former end) If a molecule had some extra positive charge on one end but also had the same amount of extra positive charge on the other end, they would cancel out and not contribute to any net dipole moment.
 
Most atoms and molecules have magnetic (dipole) moments. The electron has an intrinsic magnetic dipole moment related to "spin" (measured in Bohr magnetons), and electron orbitals have orbital magnetic dipole moments dependent on the l (lower case L) quantum number. Protons and neutrons have intrinsic dipole moments (measured in nuclear magnetons). Nuclei also have magnetic moments. However protons, neutrons, and electrons sometimes pair up so as to cancel magnetic moments. Helium in its ground state (2 protons, 2 neutrons, and 2 electrons in the 1S ground state) has no magnetic dipole moment. (Same for alpha particles.) The electron orbital dipole moment for l>=1 (L>=1) can be thought of as a current loop, although the analogy is not rigorous.