Water will only conduct electricity when it has an electrolyte present, when ions are in solution which will allow for the flow of an electric current.
Tap water is not pure water, even this has a very small amount of ions present which will allow the wate to conduct to a small degree. To improve the water's conductivity, one can use one of many very common electrolytes, for example "Salt", Sodium Chloride is a strong electrolyte.
"Strong" and "weak" when talking about electrolytes refers to their ability to break up into ions in solution. "Strong" electrolytes will completely break up into ions whereas "weak" electrolytes will not break up completely (although they will break up to a degree). An example of a weak electrolyte is acetic acid (AKA "vinegar"), this weak electrolyte will also allow for the flow of an electric current through water.
There are also "non-electrolytes" such as sugar which do not break into ions at all and will not allow for the flow an an electric current.