A solvent is something that dissolves something else - that something else is called a solute. The resulting mixture is called a solution.
Essentially, a solvent works by pulling apart solute particles and forming complexes with them. The result is a mixture in which the solute particles are mixed together with the solvent particles, typically with little clusters of solvent molecules around each solute particle.
Solvents can be solids, liquids, or gases. An example of a solid solvent is an alloy, where the metal acts as the solvent for whatever other particles are incorporated. A liquid solvent would be the water in salt water. A gaseous solvent would be the nitrogen in air, into which other gases, including oxygen, are mixed.