It means Judiciary of India is not under the control of Legislature and Executive.It is independent of the Legislature and the Executive.It takes any decision without the interference of the Legislature and the Executive.

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In our country we have executive , judiciary ,legistalive .in this when teling about judiciary  it is independent and is not under government it enjoys a free working with out the interfierence of the government.
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Indipendant judiciary means the judiciary is indipendant from the other two branches of state ligislature&exicutive.they are not under govt &do not work under their behalf.