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Distilled Water
Perfectly pure water won't conduct electricity. Most water isn't perfectly pure. It contains minuscule amounts of minerals, chemicals or salts and as these trace amounts increase, the ability of the water solution to conduct electricity will increase. But it takes a lot. Most tap water, most bottled drinking water, even most water dipped from a lake or stream contains so few impurities that the electrical conductivity of the water is small.
It's the Ions
When certain chemicals known as salts, such as sodium chloride or common table salt, are dissolved in water, the chemical bonds that held them together in solid or crystalline form are broken and they exist as ionized particles. Most highly acidic and alkaline chemicals also ionize when made into a solution with water. Ionized particles carry either positive or negative electrical particles and the presence of those particles boost the electrical conductivity of the salt solution. In general, the more ions present, the greater the conductivity. There are hundreds, if not thousands, of chemicals that can mix with water, ionize and cause the solution to become conductive.
Non-Aqueous Solutions
There are many substances that exist as liquids that do not contain water, but are solutions. Think of gasoline, alcohol, corn syrup and many others. Most of these are slightly conductive of electricity, but have only conductivity similar to tap water. One exception is the metal mercury that exists as a liquid at room temperatures. Mercury is highly conductive.
Temperature
When it comes to conducting electricity, temperature matters. Whether the conductor is metal or an ionized or non-ionized solution, the lower the temperature, the higher the conductivity. In most situations, the relative change as the temperature of the solution increases or decreases is minute.