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Water has a high dielectric constant because the water molecule have dipole moment and so it can be polarized. Under a given electric field, water tends to polarize strongly, nearly canceling out the effect of the field.
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In water the atoms contain covalent bonds which are partially ionic.  The ionic nature of Hydrogen and oxygen contribute to the dielectric constant.

When a voltage is applied across a capacitor with a slab (containing water) between the plates, then water molecules get polarized.  They get charges induced in them.  The amount of charge is high.  Thus the capacity to hold charge is high.  So its dielectric constant is high.  Dielectric constant of vacuum is 1 and in vacuum there are no charges induced.  So dielectric constant of vacuum is the lowest.

Dielectric constant is the capacity to hold charges in the medium.  It is also the (a kind of) inhibitor for electric force and electric field between two electric charges.  It reduces force and field between charges of same magnitude.

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