A substance that is used to dissolve another substance (i.e. the substance that another substance is dissolved in), known as the solute, to create a mixture known as a solution. While solvents are typically liquids (water being a classic example), there are cases of where solvents are solids. For example, the solvent in any metallic alloy is the metal that accounts for the largest percentage of the compound.

In context of cooking, your solvent will probably be water, an oil, an alcohol, or an acid. That is not to say that these will be the only cases but that these are the most likely cases. Whether you know it or not, you have almost certainly used a solvent.