For a solution to conduct electricity, the following two points are essential:
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It needs to have a substance that separates into ions - Conductivity in a solution is primarily due to the presence of free-moving charged particles. When an ionic compound dissolves in water, it separates into positive and negative ions, which can move freely and carry electric charge.
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It needs to produce a chemical reaction - While not always necessary for conductivity, the ability of a solution to conduct electricity can be enhanced by reactions that create more ions in solution. However, the key factor for conductivity remains the presence of ions.
Thus, the most critical requirement for a solution to conduct electricity is having a substance that separates into ions.